Midpoint Formula

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Geometry › Midpoint Formula

Questions 1 - 10

A line segment has an endpoint at and a midpoint at . Find the coordinates of the other endpoint.

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 .

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

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

The second endpoint must be at .

A line segment has an endpoint at and a midpoint at . Find the coordinates of the other endpoint.

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 .

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

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

The second endpoint must be at .

A line segment has endpoints at (10, 2) and (-10, -6). What is the midpoint of this line?

Explanation

Recall the formula for finding a midpoint of a line segment:

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

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{10-10}{2}, \frac{2-6}{2})=(0, -2)$

A line segment has endpoints at (10, 2) and (-10, -6). What is the midpoint of this line?

Explanation

Recall the formula for finding a midpoint of a line segment:

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

The coordinates of the midpoint is just the average of the x-coordinates and the average of the y-coordinates.

Plug in the given points to find the midpoint of the line segment.

$\text{Midpoint}=(\frac{10-10}{2}, \frac{2-6}{2})=(0, -2)$

A line segment on the coordinate plane has an endpoint at ; its midpoint is at .

True or false: Its other endpoint is located at .

True

False

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 , so the statement is true.

A line segment has an endpoint at and a midpoint at . Find the coordinates of the other endpoint.

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 .

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

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

The second endpoint must be at .

A line segment on the coordinate plane has an endpoint at ; its midpoint is at .

True or false: Its other endpoint is located at .

True

False

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 $x_{2}$ :

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