Algebra 2

Holliday, Luchin, Cuevas, Carter Marks, Day, Casey, Hayek

Chapter 10 Conic Sections - all with Video Answers

Educators

Section 1

Midpoint and Distance Formulas

00:48

Problem 1

Find the midpoint of the line segment with endpoints at the given coordinates.
$$
(-5,6),(1,7)
$$

Zach Steedman

Numerade Educator

00:43

Problem 2

Find the midpoint of the line segment with endpoints at the given coordinates.
$$
(8,9),(-3,-4.5)
$$

Zach Steedman

Numerade Educator

01:09

Problem 3

Find the midpoint of the line segment with endpoints at the given coordinates.
$$
(13,-4),(10,14.6)
$$

Zach Steedman

Numerade Educator

00:53

Problem 4

Find the midpoint of the line segment with endpoints at the given coordinates.
$$
(-12,-2),(-3.5,-7)
$$

Zach Steedman

Numerade Educator

01:04

Problem 5

Find the distance between each pair of points with the given coordinates.
$$
(2,-4),(10,-10)
$$

Zach Steedman

Numerade Educator

01:02

Problem 6

Find the distance between each pair of points with the given coordinates.
$$
(7,8),(-4,9)
$$

Zach Steedman

Numerade Educator

01:40

Problem 7

Find the distance between each pair of points with the given coordinates.
$$
(0,5,1,4),(1,1,2,9)
$$

Zach Steedman

Numerade Educator

01:37

Problem 8

Find the distance between each pair of points with the given coordinates.
$$
(-4.3,2.6),(6.5,-3.4)
$$

Zach Steedman

Numerade Educator

01:22

The map of a mall is overlaid with a numeric grid. The kiosk for the cell phone store is halfway between Terry's Ice Cream and the See Clearly eyeglass store. If the ice cream store is at $(2,4)$ and the eyeglass store is at $(78,46),$ find the distance the kiosk is from the eyeglass store.

Zach Steedman

Numerade Educator

00:35

Problem 10

Find the midpoint of the line segment with endpoints at the given coordinates.
$$
(8,3),(16,7)
$$

Zach Steedman

Numerade Educator

00:46

Problem 11

Find the midpoint of the line segment with endpoints at the given coordinates.
$$
(-5,3),(-3,-7)
$$

Zach Steedman

Numerade Educator

00:31

Problem 12

Find the midpoint of the line segment with endpoints at the given coordinates.
$$
(6,-5),(-2,-7)
$$

Zach Steedman

Numerade Educator

00:44

Problem 13

Find the midpoint of the line segment with endpoints at the given coordinates.
$$
(5,9),(12,18)
$$

Zach Steedman

Numerade Educator

02:10

Problem 14

GEOMETRY Triangle MNP has vertices $M(3,5), N(-2,8),$ and $P(7,-4) .$ Find the coordinates of the midpoint of each side.

Zach Steedman

Numerade Educator

00:55

Problem 15

REAL ESTATE In John's town, the numbered streets and avenues form a grid. He belongs to a gym at the corner of 12 th Street and 15 th Avenue, and the deli where he works is at the corner of 4 th Street and 5th Avenue. He wants to rent an apartment halfway between the two. In what area should he look?

Zach Steedman

Numerade Educator

01:27

Problem 16

Find the distance between each pair of points with the given coordinates.
$$
(-4,9),(1,-3)
$$

Zach Steedman

Numerade Educator

01:29

Problem 17

Find the distance between each pair of points with the given coordinates.
$$
(1,-14),(-6,10)
$$

Zach Steedman

Numerade Educator

01:02

Problem 18

Find the distance between each pair of points with the given coordinates.
$$
(-4,-10),(-3,-11)
$$

Zach Steedman

Numerade Educator

01:07

Problem 19

Find the distance between each pair of points with the given coordinates.
$$
(9,-2),(12,-14)
$$

Zach Steedman

Numerade Educator

02:12

Problem 20

Find the distance between each pair of points with the given coordinates.
$$
(0.23,0.4),(0.68,-0.2)
$$

Zach Steedman

Numerade Educator

01:38

Problem 21

Find the distance between each pair of points with the given coordinates.
$$
(2.3,-1.2),(-4.5,3.7)
$$

Zach Steedman

Numerade Educator

05:46

Problem 22

GEOMETRY Quadrilateral RSTV has vertices $R(-4,6), S(4,5), T(6,3),$ and $V(5,-8) .$ Find the perimeter of the quadrilateral.

Sheryl Ezze

Numerade Educator

01:56

Problem 23

GEOMETRY Triangle $B C D$ has vertices $B(4,9), C(8,-9),$ and $D(-6,5) .$ Find the length of median $\frac{B P}{B P}$ . (Hint: A median connects a vertex of a triangle to the midpoint of the opposite side.)

Zach Steedman

Numerade Educator

02:45

Problem 24

Find the midpoint of the line segment with endpoints at the given coordinates. Then find the distance between the points.
$$
\left(-3,-\frac{2}{11}\right),\left(5, \frac{9}{11}\right)
$$

Zach Steedman

Numerade Educator

02:22

Problem 25

Find the midpoint of the line segment with endpoints at the given coordinates. Then find the distance between the points.
$$
\left(0, \frac{1}{5}\right),\left(\frac{3}{5},-\frac{3}{5}\right)
$$

Zach Steedman

Numerade Educator

03:08

Problem 26

Find the midpoint of the line segment with endpoints at the given coordinates. Then find the distance between the points.
$$
(2 \sqrt{3},-5),(-3 \sqrt{3}, 9)
$$

Zach Steedman

Numerade Educator

06:23

Problem 27

Find the midpoint of the line segment with endpoints at the given coordinates. Then find the distance between the points.
$$
\left(\frac{2 \sqrt{3}}{3}, \frac{\sqrt{5}}{4}\right),\left(-\frac{2 \sqrt{3}}{3}, \frac{\sqrt{5}}{2}\right)
$$

Zach Steedman

Numerade Educator

06:40

Problem 28

GEOMETRY Find the perimeter and area of the triangle at the right.

Sheryl Ezze

Numerade Educator

02:23

Problem 29

GEOMETRY A circle has a radius with endpoints at $(2,5)$ and $(-1,-4)$ . Find the circumference and
area of the circle.

Zach Steedman

Numerade Educator

02:13

Problem 30

GEOMETRY Circle $Q$ has a diameter $\overline{A B}$ . If $A$ is at $(-3,-5)$ and the center of the circle is at $(2,3),$ find the coordinates of $B$ .

Zach Steedman

Numerade Educator

01:15

Problem 31

GEOGRAPHY For Exercises 31 and $32,$ use the following information. The U.S. Geological Survey (USGS) has determined the official center of the United States.
Approximate the center of the United States. Describe vour method.

Zach Steedman

Numerade Educator

00:25

Problem 32

GEOGRAPHY For Exercises 31 and $32,$ use the following information. The U.S. Geological Survey (USGS) has determined the official center of the United States.
Use the Internet or other reference to look up the USGS geographical center of the United States. How does the location given by USGS compare to the result of your method?

Zach Steedman

Numerade Educator

02:05

Problem 33

For Exercises 33 and 34 , use the figure at the right, where a grid is superimposed on a map of a portion of the state of Alabama.
How far is it from Birmingham to Montgomery if each unit on the grid represents 40 miles?

Zach Steedman

Numerade Educator

01:32

Problem 34

For Exercises 33 and 34 , use the figure at the right, where a grid is superimposed on a map of a portion of the state of Alabama.
How long would it take a plane to fly from Huntsville to Montgomery if its average speed is 180 miles per hour?

Zach Steedman

Numerade Educator

00:47

Problem 35

A stage crew is making the set for a children's play. They want to make some gingerbread shapes out of leftover squares of wood with sides measuring 1 foot. They can make taller shapes by cutting them out of the wood diagonally. To the nearest inch, how tall is the gingerbread shape in the drawing?

Zach Steedman

Numerade Educator

00:47

Problem 36

OPEN ENDED Find two points that are $\sqrt{29}$ units apart.

Zach Steedman

Numerade Educator

04:54

Problem 37

REASONING Identify all of the points that are equidistant from the endpoints of a given segment.

Sheryl Ezze

Numerade Educator

10:04

Problem 38

Verify the Midpoint Formula. (Hint: You must show that the formula gives the coordinates of a point on the line through the given endpoints and that the point is equidistant from the endpoints.)

Sheryl Ezze

Numerade Educator

00:37

Problem 39

Explain how to use the Distance Formula to approximate the distance between two cities on a map.

Zach Steedman

Numerade Educator

00:45

Problem 40

ACT/SAT Point $D(5,-1)$ is the midpoint of segment $C E .$ If point $C$ has coordinates $(3,2),$ what are the coordinates of point $E ?$
$$
\begin{array}{l}{\mathbf{A}(8,1)} \\ {\mathbf{B}(7,-4)} \\ {\mathbf{C}(2,-3)} \\ {\mathbf{D}\left(4, \frac{1}{2}\right)}\end{array}
$$

Zach Steedman

Numerade Educator

00:30

Problem 41

REVIEW If $\log _{10} x=-3,$ what is the value of $x ?$
$$
\begin{array}{ll}{\mathbf{F} \quad x=1000} & {\mathbf{H} x=\sqrt{\frac{1}{100}}} \\ {\mathbf{G} x=\frac{1}{1000}} & {\mathbf{J} \quad x=-\sqrt{\frac{1}{100}}}\end{array}
$$

Zach Steedman

Numerade Educator

01:45