• Home
  • Textbooks
  • Precalculus: Graphs and Models, A Right Triangle Approach
  • Graphs, Functions, and Models

Precalculus: Graphs and Models, A Right Triangle Approach

Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen

Chapter 1

Graphs, Functions, and Models - all with Video Answers

Educators

Section 1

Introduction to Graphing

00:48

Problem 1

Use the following graph ( Graph can't copy)
Find the coordinates of points $A, B, C, D, E$ and $F$

Erika Bustos
Erika Bustos
Numerade Educator
00:41

Problem 2

Use the following graph ( Graph can't copy)
Find the coordinates of points $G, H, I, J, K$ and $L$

Erika Bustos
Erika Bustos
Numerade Educator
01:19

Problem 3

Graph and label the given points.
$$(4,0),(-3,-5),(-1,4),(0,2),(2,-2)$$

AG
Ankit Gupta
Numerade Educator
00:39

Problem 4

Graph and label the given points.
$$(1,4),(-4,-2),(-5,0),(2,-4),(0,3)$$

Erika Bustos
Erika Bustos
Numerade Educator
01:15

Problem 5

Graph and label the given points.
$$(-5,1),(5,1),(2,3),(2,-1),(0,1)$$

AG
Ankit Gupta
Numerade Educator
00:32

Problem 6

Graph and label the given points.
$$(0,-1),(4,-3),(-5,2),(2,0),(-1,-5)$$

Erika Bustos
Erika Bustos
Numerade Educator
00:41

Problem 7

Express the data pictured in the graph as ordered pairs, letting the first coordinate represent the year and the second coordinate the amount or percent.
(picture can't copy)

Erika Bustos
Erika Bustos
Numerade Educator
00:46

Problem 8

Express the data pictured in the graph as ordered pairs, letting the first coordinate represent the year and the second coordinate the amount or percent.
(picture can't copy)

Erika Bustos
Erika Bustos
Numerade Educator
02:00

Problem 9

Use substitution to determine whether the given ordered pairs are solutions of the given equation.
$$(-1,-9),(0,2) ; y=7 x-2$$

AG
Ankit Gupta
Numerade Educator
02:05

Problem 10

Use substitution to determine whether the given ordered pairs are solutions of the given equation.
$$\left(\frac{1}{2}, 8\right),(-1,6) ; y=-4 x+10$$

AG
Ankit Gupta
Numerade Educator
02:26

Problem 11

Use substitution to determine whether the given ordered pairs are solutions of the given equation.
$$\left(\frac{2}{3}, \frac{3}{4}\right),\left(1, \frac{3}{2}\right) ; 6 x-4 y=1$$

AG
Ankit Gupta
Numerade Educator
02:19

Problem 12

Use substitution to determine whether the given ordered pairs are solutions of the given equation.
$$(1.5,2.6),(-3,0) ; x^{2}+y^{2}=9$$

AG
Ankit Gupta
Numerade Educator
03:16

Problem 13

Use substitution to determine whether the given ordered pairs are solutions of the given equation.
$$\left(-\frac{1}{2},-\frac{4}{5}\right),\left(0, \frac{3}{5}\right) ; 2 a+5 b=3$$

AG
Ankit Gupta
Numerade Educator
02:06

Problem 14

Use substitution to determine whether the given ordered pairs are solutions of the given equation.
$$\left(0, \frac{3}{2}\right),\left(\frac{2}{3}, 1\right) ; 3 m+4 n=6$$

AG
Ankit Gupta
Numerade Educator
02:21

Problem 15

Use substitution to determine whether the given ordered pairs are solutions of the given equation.
$$(-0.75,2.75),(2,-1) ; x^{2}-y^{2}=3$$

AG
Ankit Gupta
Numerade Educator
02:18

Problem 16

Use substitution to determine whether the given ordered pairs are solutions of the given equation.
$$(2,-4),(4,-5) ; 5 x+2 y^{2}=70$$

AG
Ankit Gupta
Numerade Educator
02:10

Problem 17

Find the intercepts and then graph the line.
$$5 x-3 y=-15$$

AG
Ankit Gupta
Numerade Educator
02:03

Problem 18

Find the intercepts and then graph the line.
$$2 x-4 y=8$$

AG
Ankit Gupta
Numerade Educator
01:55

Problem 19

Find the intercepts and then graph the line.
$$2 x+y=4$$

AG
Ankit Gupta
Numerade Educator
01:57

Problem 20

Find the intercepts and then graph the line.
$$3 x+y=6$$

AG
Ankit Gupta
Numerade Educator
01:48

Problem 21

Find the intercepts and then graph the line.
$$4 y-3 x=12$$

AG
Ankit Gupta
Numerade Educator
02:29

Problem 22

Find the intercepts and then graph the line.
$$3 y+2 x=-6$$

AG
Ankit Gupta
Numerade Educator
01:52

Problem 23

Graph the equation.
$$y=3 x+5$$

AG
Ankit Gupta
Numerade Educator
00:18

Problem 24

Graph the equation.
$$y=-2 x-1$$

Lily An
Lily An
Numerade Educator
01:51

Problem 25

Graph the equation.
$$x-y=3$$

AG
Ankit Gupta
Numerade Educator
01:49

Problem 26

Graph the equation.
$$x+y=4$$

AG
Ankit Gupta
Numerade Educator
01:48

Problem 27

Graph the equation.
$$y=-\frac{3}{4} x+3$$

AG
Ankit Gupta
Numerade Educator
01:30

Problem 28

Graph the equation.
$$3 y-2 x=3$$

AG
Ankit Gupta
Numerade Educator
01:59

Problem 29

Graph the equation.
$$5 x-2 y=8$$

AG
Ankit Gupta
Numerade Educator
02:00

Problem 30

Graph the equation.
$$y=2-\frac{4}{3} x$$

AG
Ankit Gupta
Numerade Educator
02:04

Problem 31

Graph the equation.
$$x-4 y=5$$

AG
Ankit Gupta
Numerade Educator
01:32

Problem 32

Graph the equation.
$$6 x-y=4$$

AG
Ankit Gupta
Numerade Educator
01:53

Problem 33

Graph the equation.
$$2 x+5 y=-10$$

AG
Ankit Gupta
Numerade Educator
01:50

Problem 34

Graph the equation.
$$4 x-3 y=12$$

AG
Ankit Gupta
Numerade Educator
01:22

Problem 35

Graph the equation.
$$y=-x^{2}$$

AG
Ankit Gupta
Numerade Educator
01:29

Problem 36

Graph the equation.
$$y=x^{2}$$

AG
Ankit Gupta
Numerade Educator
01:22

Problem 37

Graph the equation.
$$y=x^{2}-3$$

AG
Ankit Gupta
Numerade Educator
01:19

Problem 38

Graph the equation.
$$y=4-x^{2}$$

AG
Ankit Gupta
Numerade Educator
01:56

Problem 39

Graph the equation.
$$y=-x^{2}+2 x+3$$

AG
Ankit Gupta
Numerade Educator
01:50

Problem 40

Graph the equation.
$$y=x^{2}+2 x-1$$

AG
Ankit Gupta
Numerade Educator
00:23

Problem 41

Use a graphing calculator to match the equation with one of the graphs ( $a$ )-(d) that follow.
$$y=3-x$$

Erika Bustos
Erika Bustos
Numerade Educator
00:47

Problem 42

Use a graphing calculator to match the equation with one of the graphs ( $a$ )-(d) that follow.
$$2 x-y=6$$

Erika Bustos
Erika Bustos
Numerade Educator
00:23

Problem 43

Use a graphing calculator to match the equation with one of the graphs ( $a$ )-(d) that follow.
$$y=x^{2}+2 x+1$$

Erika Bustos
Erika Bustos
Numerade Educator
00:32

Problem 44

Use a graphing calculator to match the equation with one of the graphs ( $a$ )-(d) that follow.
$$y=8-x^{2}$$

Erika Bustos
Erika Bustos
Numerade Educator
00:32

Problem 45

Use a graphing calculator to graph the equation in the standard window.
$$y=2 x+1$$

Erika Bustos
Erika Bustos
Numerade Educator
00:28

Problem 46

Use a graphing calculator to graph the equation in the standard window.
$$y=3 x-4$$

Erika Bustos
Erika Bustos
Numerade Educator
00:41

Problem 47

Use a graphing calculator to graph the equation in the standard window.
$$4 x+y=7$$

Erika Bustos
Erika Bustos
Numerade Educator
00:49

Problem 48

Use a graphing calculator to graph the equation in the standard window.
$$5 x+y=-8$$

Erika Bustos
Erika Bustos
Numerade Educator
00:30

Problem 49

Use a graphing calculator to graph the equation in the standard window.
$$y=\frac{1}{3} x+2$$

Erika Bustos
Erika Bustos
Numerade Educator
00:29

Problem 50

Use a graphing calculator to graph the equation in the standard window.
$$y=\frac{3}{2} x-4$$

Erika Bustos
Erika Bustos
Numerade Educator
01:31

Problem 51

Use a graphing calculator to graph the equation in the standard window.
$$2 x+3 y=-5$$

Erika Bustos
Erika Bustos
Numerade Educator
01:27

Problem 52

Use a graphing calculator to graph the equation in the standard window.
$$3 x+4 y=1$$

Erika Bustos
Erika Bustos
Numerade Educator
01:00

Problem 53

Use a graphing calculator to graph the equation in the standard window.
$$y=x^{2}+6$$

Erika Bustos
Erika Bustos
Numerade Educator
01:22

Problem 54

Use a graphing calculator to graph the equation in the standard window.
$$y=x^{2}-8$$

Erika Bustos
Erika Bustos
Numerade Educator
01:07

Problem 55

Use a graphing calculator to graph the equation in the standard window.
$$y=2-x^{2}$$

Erika Bustos
Erika Bustos
Numerade Educator
00:55

Problem 56

Use a graphing calculator to graph the equation in the standard window.
$$y=5-x^{2}$$

Erika Bustos
Erika Bustos
Numerade Educator
01:01

Problem 57

Use a graphing calculator to graph the equation in the standard window.
$$y=x^{2}+4 x-2$$

Erika Bustos
Erika Bustos
Numerade Educator
01:12

Problem 58

Use a graphing calculator to graph the equation in the standard window.
$$y=x^{2}-5 x+3$$

Erika Bustos
Erika Bustos
Numerade Educator
00:57

Problem 59

Graph the equation in the standard window and in the given window. Determine which window better shows the shape of the graph and the $x$ - and y-intercepts.
$$\begin{aligned}
&y=3 x^{2}-6\\
&[-4,4,-4,4]
\end{aligned}$$

Erika Bustos
Erika Bustos
Numerade Educator
00:25

Problem 60

Graph the equation in the standard window and in the given window. Determine which window better shows the shape of the graph and the $x$ - and y-intercepts.
$$\begin{aligned}
&y=-2 x+24\\
&[-15,15,-10,30], \text { with } \mathrm{Xscl}=3 \text { and } \mathrm{Yscl}=5
\end{aligned}$$

Erika Bustos
Erika Bustos
Numerade Educator
00:31

Problem 61

Graph the equation in the standard window and in the given window. Determine which window better shows the shape of the graph and the $x$ - and y-intercepts.
$$\begin{aligned}
&y=-\frac{1}{6} x^{2}+\frac{1}{12}\\
&[-1,1,-0.3,0.3], \text { with } \mathrm{Xscl}=0.1 \text { and }\\
&\mathrm{Yscl}=0.1
\end{aligned}$$

Erika Bustos
Erika Bustos
Numerade Educator
00:25

Problem 62

Graph the equation in the standard window and in the given window. Determine which window better shows the shape of the graph and the $x$ - and y-intercepts.
$$\begin{aligned}
&y=6-x^{2}\\
&[-3,3,-3,3]
\end{aligned}$$

Erika Bustos
Erika Bustos
Numerade Educator
01:49

Problem 63

Find the distance between the pair of points. Give an exact answer and, where appropriate, an approximation to three decimal places.
$$(4,6) \text { and }(5,9)$$

AG
Ankit Gupta
Numerade Educator
01:34

Problem 64

Find the distance between the pair of points. Give an exact answer and, where appropriate, an approximation to three decimal places.
$$(-3,7) \text { and }(2,11)$$

AG
Ankit Gupta
Numerade Educator
01:35

Problem 65

Find the distance between the pair of points. Give an exact answer and, where appropriate, an approximation to three decimal places.
$$(-11,-8) \text { and }(1,-13)$$

AG
Ankit Gupta
Numerade Educator
01:28

Problem 66

Find the distance between the pair of points. Give an exact answer and, where appropriate, an approximation to three decimal places.
$$(-60,5) \text { and }(-20,35)$$

AG
Ankit Gupta
Numerade Educator
01:23

Problem 67

Find the distance between the pair of points. Give an exact answer and, where appropriate, an approximation to three decimal places.
$$(6,-1) \text { and }(9,5)$$

AG
Ankit Gupta
Numerade Educator
01:19

Problem 68

Find the distance between the pair of points. Give an exact answer and, where appropriate, an approximation to three decimal places.
$$(-4,-7) \text { and }(-1,3)$$

AG
Ankit Gupta
Numerade Educator
01:41

Problem 69

Find the distance between the pair of points. Give an exact answer and, where appropriate, an approximation to three decimal places.
$$\left(-8, \frac{7}{11}\right) \text { and }\left(8, \frac{7}{11}\right)$$

AG
Ankit Gupta
Numerade Educator
01:59

Problem 70

Find the distance between the pair of points. Give an exact answer and, where appropriate, an approximation to three decimal places.
$$\left(\frac{1}{2},-\frac{4}{25}\right) \text { and }\left(\frac{1}{2},-\frac{13}{25}\right)$$

AG
Ankit Gupta
Numerade Educator
01:37

Problem 71

Find the distance between the pair of points. Give an exact answer and, where appropriate, an approximation to three decimal places.
$$\left(-\frac{3}{5},-4\right) \text { and }\left(-\frac{3}{5}, \frac{2}{3}\right)$$

AG
Ankit Gupta
Numerade Educator
01:36

Problem 72

Find the distance between the pair of points. Give an exact answer and, where appropriate, an approximation to three decimal places.
$$\left(-\frac{11}{3},-\frac{1}{2}\right) \text { and }\left(\frac{1}{3}, \frac{5}{2}\right)$$

AG
Ankit Gupta
Numerade Educator
01:39

Problem 73

Find the distance between the pair of points. Give an exact answer and, where appropriate, an approximation to three decimal places.
$$(-4.2,3) \text { and }(2.1,-6.4)$$

AG
Ankit Gupta
Numerade Educator
01:36

Problem 74

Find the distance between the pair of points. Give an exact answer and, where appropriate, an approximation to three decimal places.
$$(0.6,-1.5) \text { and }(-8.1,-1.5)$$

AG
Ankit Gupta
Numerade Educator
01:21

Problem 75

Find the distance between the pair of points. Give an exact answer and, where appropriate, an approximation to three decimal places.
$$(0,0) \text { and }(a, b)$$

AG
Ankit Gupta
Numerade Educator
01:24

Problem 76

Find the distance between the pair of points. Give an exact answer and, where appropriate, an approximation to three decimal places.
$$(r, s) \text { and }(-r,-s)$$

AG
Ankit Gupta
Numerade Educator
01:15

Problem 77

The points $(-3,-1)$ and $(9,4)$ are the endpoints of the diameter of a circle. Find the length of the radius of the circle.

Erika Bustos
Erika Bustos
Numerade Educator
01:10

Problem 78

The point $(0,1)$ is on a circle that has center $(-3,5) .$ Find the length of the diameter of the circle.

Erika Bustos
Erika Bustos
Numerade Educator
05:03

Problem 79

The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
$$(-4,5),(6,1), \text { and }(-8,-5)$$

AG
Ankit Gupta
Numerade Educator
04:16

Problem 80

The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
$$(-3,1),(2,-1), \text { and }(6,9)$$

AG
Ankit Gupta
Numerade Educator
04:44

Problem 81

The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
$$(-4,3),(0,5), \text { and }(3,-4)$$

AG
Ankit Gupta
Numerade Educator
04:06

Problem 82

The converse of the Pythagorean theorem is also a true statement: If the sum of the squares of the lengths of two sides of a triangle is equal to the square of the length of the third side, then the triangle is a right triangle. Use the distance formula and the Pythagorean theorem to determine whether the set of points could be vertices of a right triangle.
The points $(-3,4),(2,-1),(5,2),$ and $(0,7)$ are vertices of a quadrilateral. Show that the quadrilateral is a rectangle. (Hint: Show that the opposite sides of the quadrilateral are the same length and that the two diagonals are the same length.)

AG
Ankit Gupta
Numerade Educator
01:36

Problem 83

Find the midpoint of the segment having the given endpoints.
$$(4,-9) \text { and }(-12,-3)$$

AG
Ankit Gupta
Numerade Educator
01:32

Problem 84

Find the midpoint of the segment having the given endpoints.
$$(7,-2) \text { and }(9,5)$$

AG
Ankit Gupta
Numerade Educator
01:45

Problem 85

Find the midpoint of the segment having the given endpoints.
$$\left(0, \frac{1}{2}\right) \text { and }\left(-\frac{2}{5}, 0\right)$$

AG
Ankit Gupta
Numerade Educator
01:58

Problem 86

Find the midpoint of the segment having the given endpoints.
$$(0,0) \text { and }\left(-\frac{7}{13}, \frac{2}{7}\right)$$

AG
Ankit Gupta
Numerade Educator
01:47

Problem 87

Find the midpoint of the segment having the given endpoints.
$$(6.1,-3.8) \text { and }(3.8,-6.1)$$

AG
Ankit Gupta
Numerade Educator
01:44

Problem 88

Find the midpoint of the segment having the given endpoints.
$$(-0.5,-2.7) \text { and }(4.8,-0.3)$$

AG
Ankit Gupta
Numerade Educator
01:40

Problem 89

Find the midpoint of the segment having the given endpoints.
$$(-6,5) \text { and }(-6,8)$$

AG
Ankit Gupta
Numerade Educator
01:31

Problem 90

Find the midpoint of the segment having the given endpoints.
$$(1,-2) \text { and }(-1,2)$$

AG
Ankit Gupta
Numerade Educator
01:58

Problem 91

Find the midpoint of the segment having the given endpoints.
$$\left(-\frac{1}{6},-\frac{3}{5}\right) \text { and }\left(-\frac{2}{3}, \frac{5}{4}\right)$$

AG
Ankit Gupta
Numerade Educator
01:57

Problem 92

Find the midpoint of the segment having the given endpoints.
$$\left(\frac{2}{9}, \frac{1}{3}\right) \text { and }\left(-\frac{2}{5}, \frac{4}{5}\right)$$

AG
Ankit Gupta
Numerade Educator
03:38

Problem 93

Graph the rectangle described in Exercise $82 .$ Then determine the coordinates of the midpoint of each of the four sides. Are the midpoints vertices of a rectangle?

AG
Ankit Gupta
Numerade Educator
01:26

Problem 94

Graph the square with vertices $(-5,-1),(7,-6)$ $(12,6),$ and $(0,11) .$ Then determine the midpoint of each of the four sides. Are the midpoints vertices of a square?

AG
Ankit Gupta
Numerade Educator
01:50

Problem 95

The points $(\sqrt{7},-4)$ and $(\sqrt{2}, 3)$ are endpoints of the diameter of a circle. Determine the center of the circle.

AG
Ankit Gupta
Numerade Educator
01:49

Problem 96

The points $(-3, \sqrt{5})$ and $(1, \sqrt{2})$ are endpoints of the diagonal of a square. Determine the center of the square.

AG
Ankit Gupta
Numerade Educator
00:46

Problem 97

How would you change the window so that the circle is not distorted? Answers may vary.
$$(x+3)^{2}+(y-2)^{2}=36$$

Erika Bustos
Erika Bustos
Numerade Educator
00:40

Problem 98

How would you change the window so that the circle is not distorted? Answers may vary.
$$(x-4)^{2}+(y+5)^{2}=49$$

Erika Bustos
Erika Bustos
Numerade Educator
01:41

Problem 99

Find an equation for a circle satisfying the given conditions.
Center $(2,3),$ radius of length $\frac{5}{3}$

Mukesh Devi
Mukesh Devi
Numerade Educator
01:27

Problem 100

Find an equation for a circle satisfying the given conditions.
Center $(4,5),$ diameter of length 8.2

AG
Ankit Gupta
Numerade Educator
01:52

Problem 101

Find an equation for a circle satisfying the given conditions.
Center $(-1,4),$ passes through $(3,7)$

AG
Ankit Gupta
Numerade Educator
02:41

Problem 102

Find an equation for a circle satisfying the given conditions.
Center $(6,-5),$ passes through $(1,7)$

AG
Ankit Gupta
Numerade Educator
03:01

Problem 103

Find an equation for a circle satisfying the given conditions.
The points $(7,13)$ and $(-3,-11)$ are at the ends of a diameter.

AG
Ankit Gupta
Numerade Educator
03:36

Problem 104

Find an equation for a circle satisfying the given conditions.
The points $(-9,4),(-2,5),(-8,-3),$ and $(-1,-2)$ are vertices of an inscribed square.

AG
Ankit Gupta
Numerade Educator
02:49

Problem 105

Find an equation for a circle satisfying the given conditions.
Center $(-2,3),$ tangent (touching at one point) to the $y$ -axis

AG
Ankit Gupta
Numerade Educator
03:01

Problem 106

Find an equation for a circle satisfying the given conditions.
Center $(4,-5),$ tangent to the $x$ -axis

AG
Ankit Gupta
Numerade Educator
00:40

Problem 107

Find the center and the radius of the circle. Then graph the circle by hand. Check your graph with a graphing calculator:
$$x^{2}+y^{2}=4$$

Erika Bustos
Erika Bustos
Numerade Educator
00:59

Problem 108

Find the center and the radius of the circle. Then graph the circle by hand. Check your graph with a graphing calculator:
$$x^{2}+y^{2}=81$$

Erika Bustos
Erika Bustos
Numerade Educator
00:51

Problem 109

Find the center and the radius of the circle. Then graph the circle by hand. Check your graph with a graphing calculator:
$$x^{2}+(y-3)^{2}=16$$

Erika Bustos
Erika Bustos
Numerade Educator
01:11

Problem 110

Find the center and the radius of the circle. Then graph the circle by hand. Check your graph with a graphing calculator:
$$(x+2)^{2}+y^{2}=100$$

Erika Bustos
Erika Bustos
Numerade Educator
00:55

Problem 111

Find the center and the radius of the circle. Then graph the circle by hand. Check your graph with a graphing calculator:
$$(x-1)^{2}+(y-5)^{2}=36$$

Erika Bustos
Erika Bustos
Numerade Educator
01:07

Problem 112

Find the center and the radius of the circle. Then graph the circle by hand. Check your graph with a graphing calculator:
$$(x-7)^{2}+(y+2)^{2}=25$$

Erika Bustos
Erika Bustos
Numerade Educator
00:55

Problem 113

Find the center and the radius of the circle. Then graph the circle by hand. Check your graph with a graphing calculator:
$$(x+4)^{2}+(y+5)^{2}=9$$

Erika Bustos
Erika Bustos
Numerade Educator
01:00

Problem 114

Find the center and the radius of the circle. Then graph the circle by hand. Check your graph with a graphing calculator:
$$(x+1)^{2}+(y-2)^{2}=64$$

Erika Bustos
Erika Bustos
Numerade Educator
01:42

Problem 115

Find the equation of the circle.
(graph can't copy)

Vishal Parmar
Vishal Parmar
Numerade Educator
01:42

Problem 116

Find the equation of the circle.
(graph can't copy)

Vishal Parmar
Vishal Parmar
Numerade Educator
01:42

Problem 117

Find the equation of the circle.
(graph can't copy)

Vishal Parmar
Vishal Parmar
Numerade Educator
01:42

Problem 118

Find the equation of the circle.
(graph can't copy)

Vishal Parmar
Vishal Parmar
Numerade Educator
02:38

Problem 119

To the student and the instructor: The Synthesis exercises found at the end of every exercise set challenge students to combine concepts or skills studied in that section or in preceding parts of the text.
If the point $(p, q)$ is in the fourth quadrant, in which quadrant is the point $(q,-p) ?$

Charles Machakwa
Charles Machakwa
Numerade Educator
02:39

Problem 120

Find the distance between the pair of points and find the midpoint of the segment having the given points as endpoints.
$$\left(a, \frac{1}{a}\right) \text { and }\left(a+h, \frac{1}{a+h}\right)$$

AG
Ankit Gupta
Numerade Educator
02:40

Problem 121

Find the distance between the pair of points and find the midpoint of the segment having the given points as endpoints.
$$(a, \sqrt{a}) \text { and }(a+h, \sqrt{a+h})$$

AG
Ankit Gupta
Numerade Educator
01:42

Problem 122

Find an equation of a circle satisfying the given conditions.
Center $(-5,8)$ with a circumference of $10 \pi$ units

AG
Ankit Gupta
Numerade Educator
01:32

Problem 123

Find an equation of a circle satisfying the given conditions.
Center $(2,-7)$ with an area of $36 \pi$ square units

AG
Ankit Gupta
Numerade Educator
04:44

Problem 124

Find an equation of a circle satisfying the given conditions.
Find the point on the $x$ -axis that is equidistant from the points $(-4,-3)$ and $(-1,5)$

Charles Machakwa
Charles Machakwa
Numerade Educator
03:45

Problem 125

Find an equation of a circle satisfying the given conditions.
Find the point on the $y$ -axis that is equidistant from the points $(-2,0)$ and $(4,6)$

Maria Santiago
Maria Santiago
Numerade Educator
04:58

Problem 126

Find an equation of a circle satisfying the given conditions.
Determine whether the points $(-1,-3),(-4,-9)$ and $(2,3)$ are collinear.

Maria Santiago
Maria Santiago
Numerade Educator
09:03

Problem 127

An Arch of a Circle in Carpentry. Matt is remodeling the front entrance to his home and needs to cut an arch for the top of an entranceway. The arch must be
$8 \mathrm{ft}$ wide and $2 \mathrm{ft}$ high. To draw the arch, he will use a stretched string with chalk attached at one end as a compass.
a) Using a coordinate system, locate the center of the circle.
b) What radius should Matt use to draw the arch?

Derek Follett
Derek Follett
Numerade Educator
03:28

Problem 128

Consider any right triangle with base $b$ and height $h$ situated as shown. Show that the midpoint of the hypotenuse $P$ is equidistant from the three vertices of the triangle.

AG
Ankit Gupta
Numerade Educator
00:46

Problem 129

Determine whether each of the following points lies on the unit circle, $x^{2}+y^{2}=1$
(graph can't copy)
$$\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right)$$

Erika Bustos
Erika Bustos
Numerade Educator
00:26

Problem 130

Determine whether each of the following points lies on the unit circle, $x^{2}+y^{2}=1$
(graph can't copy)
$$(0,-1)$$

Erika Bustos
Erika Bustos
Numerade Educator
00:42

Problem 131

Determine whether each of the following points lies on the unit circle, $x^{2}+y^{2}=1$
(graph can't copy)
$$\left(-\frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}\right)$$

Erika Bustos
Erika Bustos
Numerade Educator
00:36

Problem 132

Determine whether each of the following points lies on the unit circle, $x^{2}+y^{2}=1$
(graph can't copy)
$$\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)$$

Erika Bustos
Erika Bustos
Numerade Educator
02:11

Problem 133

Determine whether each of the following points lies on the unit circle, $x^{2}+y^{2}=1$
(graph can't copy)
Prove the midpoint formula by showing that $\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$ is equidistant from the points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$

AG
Ankit Gupta
Numerade Educator