Midpoint Formula - Algebra

Card 0 of 792

Question

Find the midpoint of the line segment that has endpoints at $(-2, 6)\text{ and }(-8, 10)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

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

$\text{Midpoint}=\left(\frac{-2+(-8)}{2}, \frac{6+10}{2}\right)=(-5, 8)$

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Question

Find the midpoint of a line segment that has endpoints at $\left(\frac{1}{2}, 6\right)$ and $\left(-\frac{7}{2}, 18\right)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

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

$\text{Midpoint}=\left(\frac{\frac{1}{2}+(-\frac{7}{2})}{2}, \frac{6+18}{2}\right)=\left(-\frac{3}{2},12\right)$

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Question

Find the midpoint of the line segment that has endpoints at $(100, 5)\text{ and }(2, 0)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

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

$\text{Midpoint}=\left(\frac{100+2}{2}, \frac{5+0}{2}\right)=\left(51, \frac{5}{2}\right)$

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Question

Find the midpoint of the line segment that has endpoints at $(-5, -2)\text{ and }(-9, -10)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

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

$\text{Midpoint}=\left(\frac{-5+(-9)}{2}, \frac{-2+(-10)}{2}\right)=(-7, -6)$

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Question

Find the midpoint of the line segment that has endpoints at $(1, -2)\text{ and }(7, -12)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

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

$\text{Midpoint}=\left(\frac{1+7}{2}, \frac{-2+(-12)}{2}\right)=(4, -7)$

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Question

Find the midpoint of the line segment that has endpoints at $(-0.9, 1)\text{ and }(0.1, 5)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

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

$\text{Midpoint}=\left(\frac{-0.9+0.1}{2}, \frac{1+5}{2}\right)=(-0.4, 3)$

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Question

Find the midpoint of a line segment that has endpoints at $(11, -5)\text{ and }(1, -9)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

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

$\text{Midpoint}=\left(\frac{11+1}{2}, \frac{-5+(-9)}{2}\right)=(6, -7)$

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Question

Find the midpoint of a line segment that has endpoints at $(-7, 12)\text{ and }(-3, -2)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

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

$\text{Midpoint}=\left(\frac{-7+(-3)}{2}, \frac{12+(-2)}{2}\right)=(-5, 5)$

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Question

Find the midpoint of the line segment with the endpoints $(1, 2)\text{ and }(3, 9)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

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

$\text{Midpoint}=\left(\frac{1+3}{2}, \frac{2+9}{2}\right)=\left(2, \frac{11}{2}\right)$

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Question

Find the midpoint of the line segment that has endpoints at $(8, 7)\text{ and }(2, 7)$ .

Answer

To find the midpoint of a line segment, take the average of the x-coordinates and the average of the y-coordinates.

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

$\text{Midpoint}=\left(\frac{8+2}{2}, \frac{7+7}{2}\right)=(5, 7)$

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Question

What is the midpoint of a line that connects the points and ?

Answer

The midpoint formula is $\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$ .

Therefore, all we need to do is plug in the points given to us to find the midpoint.

In this case, $x_{1}=1,x_{2}=-7,y_{1}=5,y_{2}=9$ .

To find the -value for the midpoint, we add: . Then we divide by : .

To find the -value for the midpoint, we add: . Then we divide by : .

So our solution is .

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Question

Find the midpoint of the given points:

Answer

To solve for the midpoint, we want to plug in our coordinate values into the midpoint formula:

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})$

$(\frac{-1+3}{2},\frac{2+6}{2})=(\frac{2}{2},\frac{8}{2})=(1,4)$

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Question

Find the midpoint of the given set of coordinates:

Answer

To find the midpoint, we must plug in the values for both points into the midpoint formula:

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})=(\frac{-5+3}{2},\frac{2+-4}{2})=(\frac{-2}{2},\frac{-2}{2})=(-1,-1)$

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Question

What is the midpoint of a line segment with the end points and ?

Answer

In order to solve for the midpoint of a line segment when the end points are given, the x and y values must be averaged.

A formula for this would be:
$midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

This probem may be quickly solved for by substituting in the given information.

$midpoint=(\frac{1+7}{2},\frac{2+8}{2})$

$midpoint=(\frac{8}{2},\frac{10}{2})$

$midpoint={\color{Blue} (4,5)}$

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Question

Find the midpoint of a line segment with and as its endpoints.

Answer

In order to solve for the midpoint of a line segment when the end points are given, the x and y values must be averaged.

A formula for this would be:
$midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

This probem may be quickly solved for by substituting in the given information.

$midpoint=(\frac{0+10}{2},\frac{0+4}{2})$

$midpoint=(\frac{10}{2},\frac{4}{2})$

$midpoint={\color{Blue} (5,2)}$

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Question

A line segment has the endpoints and . What's the midpoint of the line segment?

Answer

In order to solve for the midpoint of a line segment when the end points are given, the x and y values must be averaged.

A formula for this would be:
$midpoint=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

This probem may be quickly solved for by substituting in the given information.

$midpoint=(\frac{20+100}{2},\frac{40+26}{2})$

$midpoint=(\frac{120}{2},\frac{66}{2})$

$midpoint={\color{Blue} (60,33)}$

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Question

What is the midpoint of a line segment AB is A is at and B is at ?

Answer

This kind of problem can be quickly solved for by using the midpoint formula:

$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$ where (x1,y1) and (x2,y2). Either of the endpoints may be assigned as either coordinate point.

Substituting in the information,

$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

$\left(\frac{3+17}{2}, \frac{4+2}{2}\right)$

$\left(\frac{20}{2}, \frac{6}{2}\right)$

${\color{Blue} (10,3)}$

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Question

Find the midpoint of a line segment with the endpoints $\small (-3,-12)$ and $\small (27,-30)$ .

Answer

This kind of problem can be quickly solved for by using the midpoint formula:

$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$ where $\small (x_1,y_1)$ and $\small (x_2,y_2)$ . Either of the endpoints may be assigned as either coordinate point.

Substituting in the information,

$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$

$\left(\frac{-3+27}{2}, \frac{-30-12}{2}\right)$

$\left(\frac{24}{2}, \frac{-42}{2}\right)$

${\color{Blue} (12,-21)}$

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Question

Find the midpoint of the line segment with the following endpoints: .

Answer

To find the midpoint of this segment, we plug the values of our respective coordinates into the midpoint formula:

$\left(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2}\right)$

$\left(\frac{0+2}{2},\frac{7+1}{2}\right)$

Simplify.

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Question

Find the midpoint of the line segment with endpoints and .

Answer

Use the midpoint formula:

$\left ( \frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}} \right )$

Substitute:

$\frac{x_{1}+x_{2}}{2} =\frac{3.6+7.2}{2} = \frac{10.8}{2} = 5.4$

$\frac{y_{1}+y_{2}}{2}} \right = \frac{9.1+(-1.5)}{2}} = \frac{7.6}{2} = 3.8$

The midpoint is

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