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Intermediate Geometry : Midpoint Formula

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Example Question #51 : Midpoint Formula

A line segment has an endpoint at (8, -2) and midpoint at (1, -1) . Find the coordinates of the other endpoint.

Possible Answers:

(2, 0)

(-5, 0)

(-6, 0)

(2, 10)

Correct answer:

(-6, 0)

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:

$\frac{8+x_2}{2}=1$

Solve for x_2 .

8+x_2=2

x_2=-6

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

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

-2+y_2=-2

y_2=0

The second endpoint must be at (-6, 0) .

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Example Question #52 : Midpoint Formula

A line segment has an endpoint at (9, -3) and midpoint at (12, -8) . Find the coordinates of the other endpoint.

Possible Answers:

(16, -21)

(17, -18)

(15, -13)

(19, -4)

Correct answer:

(15, -13)

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:

$\frac{9+x_2}{2}=12$

Solve for x_2 .

9+x_2=24

x_2=15

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

$\frac{-3+y_2}{2}=-8$

-3+y_2=-16

y_2=-13

The second endpoint must be at (15, -13) .

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Example Question #53 : Midpoint Formula

A line segment has an endpoint at (17, 2) and midpoint at (6, 8) . Find the coordinates of the other endpoint.

Possible Answers:

(18, 17)

(18, 20)

(16, 12)

(15, 14)

Correct answer:

(15, 14)

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:

$\frac{17+x_2}{2}=6$

Solve for x_2 .

17+x_2=32

x_2=15

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

$\frac{2+y_2}{2}=8$

2+y_2=16

y_2=14

The second endpoint must be at (15, 14) .

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Example Question #54 : Midpoint Formula

A line segment has an endpoint at (-2, 4) and a midpoint at (12, 2) . Find the other endpoint.

Possible Answers:

(30, 4)

(28, -2)

(-14, 22)

(26, 0)

Correct answer:

(26, 0)

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:

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

Solve for x_2 .

-2+x_2=24

x_2=26

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

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

4+y_2=4

y_2=0

The second endpoint must be at (26, 0) .

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Example Question #55 : Midpoint Formula

A line segment on the coordinate plane has an endpoint at (3.8, -1.7) ; its midpoint is at (9.2, 5.5) .

True or false: Its other endpoint is located at (14.6,12.7 ) .

Possible Answers:

False

True

Correct answer:

True

Explanation:

The midpoint of a line segment with endpoints $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is located at $\left ( \frac{x_{1}+x_{2}}{2} , \frac{y_{1}+ y_{2}}{2} \right )$ .

Therefore, set

$\frac{x_{1}+x_{2}}{2} = 9.2$ and $\frac{y_{1}+ y_{2}}{2} = 5.5$

In the first equation, set $x_{2} = 3.8$ and solve for $x_{1}$ :

$\frac{x_{1}+3.8}{2} = 9.2$

Multiply both sides by 2:

$\frac{x_{1}+3.8}{2} \cdot 2 = 9.2 \cdot 2$

$x_{1}+3.8= 18.4$

Subtract 3.8 from both sides:

$x_{1}+3.8- 3.8 = 18.4 - 3.8$

$x_{1} = 14.6$

In the second equation, set $y_{2} = -1.7$ and solve for $x_{2}$ :

$\frac{y_{1}+ (-1.7)}{2} = 5.5$

Multiply both sides by 2:

$\frac{y_{1} -1.7}{2} \cdot 2 = 5.5 \cdot 2$

$y_{1} -1.7 = 11$

Add 1.7 to both sides:

$y_{1} -1.7+ 1.7 = 11 + 1.7$

$y_{1} = 12.7$

The other endpoint is indeed at (14.6,12.7 ) , so the statement is true.

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Intermediate Geometry : Midpoint Formula

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #51 : Midpoint Formula

Example Question #52 : Midpoint Formula

Example Question #53 : Midpoint Formula

Example Question #54 : Midpoint Formula

Example Question #55 : Midpoint Formula

All Intermediate Geometry Resources

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