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Intermediate Geometry : Coordinate Geometry

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Example Questions

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Example Question #11 : How To Find The Endpoints Of A Line Segment

A line with endpoints of (-2, -9) and (x, y) has a midpoint of (-2, 6) . What are the coordinates of the unknown endpoint?

Possible Answers:

(2, -16)

(2, -20)

(-2, 21)

(-2, 14)

Correct answer:

(-2, 21)

Explanation:

Recall how to find the midpoint of a line:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{-2+x}{2}=-2$

-2+x=-4

x=-2

Now, let's solve for the coordinate.

$\frac{-9+y}{2}=6$

-9+y=12

y=21

The coordinate for the other endpoint must be (-2, 21) .

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Example Question #41 : Coordinate Geometry

A line with endpoints of (-8, 2) and (x, y) has a midpoint of (3, 5) . What are the coordinates of the unknown endpoint?

Possible Answers:

(16, 2)

(14, 8)

(9, 15)

(15, 2)

Correct answer:

(14, 8)

Explanation:

Recall how to find the midpoint of a line:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

In other words, the coordinates of the midpoint are just the average of the and coordinates of the endpoints.

We can then solve for the coordinate of the second endpoint.

Let's start with the coordinate by using the given midpoint and endpoint.

$\frac{-8+x}{2}=3$

-8+x=6

x=14

Now, let's solve for the coordinate.

$\frac{2+y}{2}=5$

2+y=10

y=8

The coordinate for the other endpoint must be (14, 8) .

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Example Question #13 : How To Find The Endpoints Of A Line Segment

A line segment has an endpoint at (-3, 1) and a midpoint at (2, -10) . Find the coordinates of the other endpoint.

Possible Answers:

(-3, -10)

(9, -19)

(7, -21)

(12, 4)

Correct answer:

(7, -21)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{-3+x_2}{2}=2$

Solve for x_2 .

-3+x_2=4

x_2=7

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{1+y_2}{2}=-10$

1+y_2=-20

y_2=-21

The second endpoint must be at (7, -21) .

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Example Question #14 : How To Find The Endpoints Of A Line Segment

A line segment has an endpoint at (5, 7) and a midpoint at (-12, 20) . Find the coordinates of the other midpoint.

Possible Answers:

(-29, 33)

(-25, 40)

(-22, 21)

(-27, 40)

Correct answer:

(-29, 33)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{5+x_2}{2}=-12$

Solve for x_2 .

5+x_2=-24

x_2=-29

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{7+y_2}{2}=20$

7+y_2=40

y_2=33

The second endpoint must be at (-29, 33) .

Report an Error

Example Question #21 : How To Find The Endpoints Of A Line Segment

A line segment has an endpoint at (11, -2) and a midpoint at (5, 0) . Find the coordinates of the other endpoint.

Possible Answers:

(-1, 2)

(3, -2)

(-1, 0)

(2, 1)

Correct answer:

(-1, 2)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{11+x_2}{2}=5$

Solve for x_2 .

11+x_2=10

x_2=-1

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{-2+y_2}{2}=0$

-2+y_2=0

y_2=2

The second endpoint must be at (-1, 2) .

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Example Question #22 : How To Find The Endpoints Of A Line Segment

A line segment has an endpoint at (-24, 12) and midpoint at (30, -5) . Find the coordinates of the other endpoint.

Possible Answers:

(92, -15)

(90, -24)

(84, -22)

(80, -40)

Correct answer:

(84, -22)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{-24+x_2}{2}=30$

Solve for x_2 .

-24+x_2=60

x_2=84

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{12+y_2}{2}=-5$

12+y_2=-10

y_2=-22

The second endpoint must be at (84, -22) .

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Example Question #23 : How To Find The Endpoints Of A Line Segment

A line segment has an endpoint at (1, 7) and midpoint at (5, 0) . Find the coordinates of the other endpoint.

Possible Answers:

(10, -2)

(9, -7)

(8, -6)

(12, -9)

Correct answer:

(9, -7)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{1+x_2}{2}=5$

Solve for x_2 .

1+x_2=10

x_2=9

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{7+y_2}{2}=0$

7+y_2=0

y_2=-7

The second endpoint must be at (9 -7) .

Report an Error

Example Question #24 : How To Find The Endpoints Of A Line Segment

A line segment has an endpoint at (-2, 5) and midpoint at (11, 2) . Find the coordinates of the other endpoint.

Possible Answers:

(22, -2)

(19, 1)

(26, -10)

(24, -1)

Correct answer:

(24, -1)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{-2+x_2}{2}=11$

Solve for x_2 .

-2+x_2=22

x_2=24

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{5+y_2}{2}=2$

5+y_2=4

y_2=-1

The second endpoint must be at (24, -1) .

Report an Error

Example Question #25 : How To Find The Endpoints Of A Line Segment

A line segment has an endpoint at (-2, -4) and midpoint at (-5, 0) . Find the coordinates of the other endpoint.

Possible Answers:

(-8, 4)

(2, 4)

(-10, 8)

(-12, 12)

Correct answer:

(-8, 4)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{-2+x_2}{2}=-5$

Solve for x_2 .

-2+x_2=-10

x_2=-8

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{-4+y_2}{2}=0$

-4+y_2=0

y_2=4

The second endpoint must be at (-8, 4) .

Report an Error

Example Question #26 : How To Find The Endpoints Of A Line Segment

A line segment has an endpoint at (3, 16) and midpoint at (14, 7) . Find the coordinates of the other endpoint.

Possible Answers:

(25, -2)

(15, -2)

(2, -12)

(27, -3)

Correct answer:

(25, -2)

Explanation:

Recall how to find the midpoint of a line segment:

$\text{Midpoint}=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$ ,

where $(x_1, y_1)\text{ and}(y_1, y_2)$ are the endpoints.

Let's first focus on the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{3+x_2}{2}=14$

Solve for x_2 .

3+x_2=28

x_2=25

Next, find the coordinate of the other endpoint. Using the information given by the question, we can write the following equation:

$\frac{16+y_2}{2}=7$

16+y_2=14

y_2=-2

The second endpoint must be at (25, -2) .

Report an Error

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Intermediate Geometry : Coordinate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #11 : How To Find The Endpoints Of A Line Segment

Example Question #41 : Coordinate Geometry

Example Question #13 : How To Find The Endpoints Of A Line Segment

Example Question #14 : How To Find The Endpoints Of A Line Segment

Example Question #21 : How To Find The Endpoints Of A Line Segment

Example Question #22 : How To Find The Endpoints Of A Line Segment

Example Question #23 : How To Find The Endpoints Of A Line Segment

Example Question #24 : How To Find The Endpoints Of A Line Segment

Example Question #25 : How To Find The Endpoints Of A Line Segment

Example Question #26 : How To Find The Endpoints Of A Line Segment

All Intermediate Geometry Resources

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