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Discovering Algebra: An Investigative Approach

Jerald Murdock, Ellen Kamischke, Eric Kamischke

Chapter 11

Introduction to Geometry - all with Video Answers

Educators

Section 1

Parallel and Perpendicular

01:51

Problem 1

Find the slope of each line.
a. $y=0.8(x-4)+7$
b. $y=5-2 x$
c. $y=-1.25(x-3)+1$
d. $y=-4+2 x$
e. $6 x-4 y=11$ (a
f. $3 x+2 y=12$
g. $-9 x+6 y=-4$
(a)
h. $10 x-15 y=7$

Nick Johnson
Nick Johnson
Numerade Educator
13:44

Problem 2

Determine whether each pair of lines is parallel, perpendicular, or neither. Verify by graphing on your calculator using a square window. [ See Calculator Note 11A. ( $\hbar$ )
a. $y=0.8(x-4)+7$
b. $y=5-2 x$
$y=-1.25(x-3)+1$
$y=-4+2 x$
c. $6 x-4 y=11$
d. $3 x+2 y=12$
$-9 x+6 y=-4$
$10 x-15 y=7$

Tp Sarathy
Tp Sarathy
Numerade Educator
00:33

Problem 3

Line $\ell$ has slope $1.2$. What is the slope of line $p$ that is parallel to line $\ell$ ?

Katelyn Chen
Katelyn Chen
Numerade Educator
01:27

Problem 4

Line $\ell$ has slope 1 .2. Line $m$ is perpendicular to line $\ell$.
a. What is the slope of line $m$ ?
(a)
b. What is the product of the slopes of line $\ell$ and line $m$ ?
(a)

Jennifer Stoner
Jennifer Stoner
Numerade Educator
03:43

Problem 5

Find the equation in point-slope form of the line that passes through $(8,-2)$ and is perpendicular to $y=3 x+7$.

Erin Kearney
Erin Kearney
Numerade Educator
02:39

Problem 6

Name each quadrilateral using the most specific term that describes it: square, rectangle, parallelogram, right trapezoid, or trapezoid.

Anna Jones
Anna Jones
Numerade Educator
06:16

Problem 7

Plot each set of points on graph paper and connect them to form a polygon. Classify each polygon using the most specific term that describes it. Use deductive reasoning to justify your answers by finding the slopes of the sides of the polygons.
$$
(-5,0),(1,4),(6,3),(-3,-3)
$$

Gladys Fowler
Gladys Fowler
Numerade Educator
01:52

Problem 8

Plot each set of points on graph paper and connect them to form a polygon. Classify each polygon using the most specific term that describes it. Use deductive reasoning to justify your answers by finding the slopes of the sides of the polygons.
$$
(-3,-2),(3,1),(5,-3),(-1,-6)
$$

Teresa Fuston
Teresa Fuston
Numerade Educator
01:52

Problem 9

Plot each set of points on graph paper and connect them to form a polygon. Classify each polygon using the most specific term that describes it. Use deductive reasoning to justify your answers by finding the slopes of the sides of the polygons.
$$
(-3,4),(0,4),(3,0),(3,-4)
$$

Teresa Fuston
Teresa Fuston
Numerade Educator
02:53

Problem 10

Plot each set of points on graph paper and connect them to form a polygon. Classify each polygon using the most specific term that describes it. Use deductive reasoning to justify your answers by finding the slopes of the sides of the polygons.
$$
(-1,4),(2,7),(5,-2),(2,-5)
$$

Gladys Fowler
Gladys Fowler
Numerade Educator
01:52

Problem 11

Plot each set of points on graph paper and connect them to form a polygon. Classify each polygon using the most specific term that describes it. Use deductive reasoning to justify your answers by finding the slopes of the sides of the polygons.
$$
(-4,-1),(-2,7),(2,6),(3,3)
$$

Teresa Fuston
Teresa Fuston
Numerade Educator
01:52

Problem 12

Plot each set of points on graph paper and connect them to form a polygon. Classify each polygon using the most specific term that describes it. Use deductive reasoning to justify your answers by finding the slopes of the sides of the polygons.
$$
(0,4),(2,8),(6,-2),(2,-1)
$$

Teresa Fuston
Teresa Fuston
Numerade Educator
02:15

Problem 13

Plot each set of points on graph paper and connect them to form a polygon. Classify each polygon using the most specific term that describes it. Use deductive reasoning to justify your answers by finding the slopes of the sides of the polygons.
$$
(-8,-2),(-4,4),(5,-2),(1,-8)
$$

Ruth Wells
Ruth Wells
Numerade Educator
01:52

Problem 14

Plot each set of points on graph paper and connect them to form a polygon. Classify each polygon using the most specific term that describes it. Use deductive reasoning to justify your answers by finding the slopes of the sides of the polygons.
$$
(-2,2),(1,5),(4,2),(1,-3)
$$

Teresa Fuston
Teresa Fuston
Numerade Educator
01:31

Problem 15

Al says you can define a right trapezoid as a
quadrilateral with exactly two right angles.
Provide a counterexample by naming four points for the vertices of a quadrilateral that has two right angles but is not a right trapezoid. Draw a sketch of your figure.

Debasish Das
Debasish Das
Numerade Educator
04:09

Problem 16

For each situation, identify whether inductive or deductive reasoning is used. Then state the hypothesis and conclusion.
a. The dinosaur Tyrannosaurus rex had sharp teeth. Animals with sharp teeth eat meat. Meat-eating animals are called carnivores. Therefore, Tyrannosaurus rex was a carnivore.
b. Krystal adds $5+6$ and gets 11 . Then she adds $13+14$ and gets 27 . Then she adds $92+93$ and gets 185 . Krystal concludes that the sum of any two consecutive integers is odd.
c. Kendra uses the properties of numbers to show that $2(x-3)=10$ is equivalent to $x=8$.

Chris Trentman
Chris Trentman
Numerade Educator
01:14

Problem 17

Multiply and combine like terms.
a. $x(x+2)(2 x-1)$ (a)
b. $(0.1 x-2.1)(0.1 x+2.1)$
(a)

Shreya Kelly
Shreya Kelly
Numerade Educator
00:58

Problem 18

Find the value halfway between
a. 3 and 11
b. $-4$ and 7
c. $-12$ and $-1$
d. 2 and 47

Charles Carter
Charles Carter
Numerade Educator