Midpoint Formula - SAT Math

Card 0 of 64

Question

What is the midpoint of the points (3,12) and (9,15)?

Answer

To find the midpoint we must know the midpoint formula which is

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

We then take the -coordinate from the first point and plug it into the formula as $x_{1}$ .

We take the -coordinate from the second point and plug it into the formula as $x_{2}$ .

We then do the same for $y_{1}$ and $y_{2}$ .

With all of the points plugged in our equation will look like this.

$(\frac{3+9}{2},\frac{12+15}{2})$

We then perform the necessary addition and division to get the answer of

$(\frac{12}{2},\frac{27}{2})=(6,13.5)$

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Question

Find the midpoint of the line segment with these endpoints: and .

Answer

The midpoint formula is

$\left(\frac{x_{1}+x_{2}}2,\frac{y_{1}+y_2}{2}\right)$ .

Add the two values together and divide the total by two to find the value of the midpoint. Add the two values together and divide the total by two to find the value of the midpoint.

$\ \left(\frac{5+9}2,\frac{7+15}{2}\right)\ \=\left(\frac{14}{2},\frac{22}{2} \right )\ \=(7,11)$

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Question

Find the midpoint of the line segment that connects the two points below.

Point 1:

Point 2:

Answer

The average of the the -coordinates and the average of the y-coordinates of the given points will give you the mid-point of the line that connects the points.

$\textup{midpoint}=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ , where is and is .

$(\frac{(0)+(-2)}{2}, \frac{(-3)+(4)}{2})$

$(\frac{-2}{2},\frac{1}{2})$

$(-1, \frac{1}{2})$

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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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Question

What is the midpoint between $\left ( 2,3\right )$ and $\left ( -7,4\right )$ ?

Answer

The formula to find the midpoint is as follows:

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

In our case our

our

substituting in these values we get

midpoint = $\left(\frac{2+-7}{2}, \frac{3+4}{2}\right)=\left(\frac{-5}{2}, \frac{7}{2}\right)$

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Question

Find the midpoint of the line that passes through the points and .

Answer

Recall the midpoint formula as $(\frac{x1+x2}{2}, \frac{y1+y2}{2})$ .

Thus,

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

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Question

Find the midpoint of the line that passes through the points and .

Answer

Recall the midpoint formula as $(\frac{x1+x2}{2}, \frac{y1+y2}{2})$ .

Thus,

$(\frac{2+(-2)}{2},\frac{-1+1}{2}) = (0,0)$

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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 a line with the endpoings (3, 4) and (-1, -1).

Answer

When finding the midpoint between two points, we use the midpoint formula

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

where and are the points given.

Knowing this, we can substitute the values into the formula. We get

$\left(\frac{3 + -1}{2}, \frac{4 + - 1}{2}\right)$

$\left(\frac{3-1}{2}, \frac{4-1}{2}\right)$

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

$\left(1, \frac{3}{2}\right)$

Therefore, $\left(1, \frac{3}{2}\right)$ is the midpoint.

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Question

A line is connected by points and on a graph. What is the midpoint?

Answer

Write the midpoint formula.

$(x,y) = (\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})$

Let and .

Substitute the given points.

$(x,y) = (\frac{2+(-1)}{2}, \frac{5+3}{2})$

Simplify the coordinate.

$(x,y) =(\frac{1}{2},4)$

The answer is: $(\frac{1}{2},4)$

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Question

What is the midpoint between $\left ( 1,3\right )$ and $\left ( 5,9\right )$ ?

Answer

To find the midpoint of two points you find the average of both the values and values.

For ,

$\frac{1+5}{2}=3$ .

For ,

$\frac{3+9}{2}=6$ .

This means the midpoint is $\left ( 3,6\right )$ .

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Question

Find the midpoint between (2,8) and (8,6).

Answer

The midpoint formula says that:

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

Given (2,8) and (8,6); $\small x_{1}=2$ $\small \small x_{2}=8$ $\small \small y_{1}=8$ $\small \small y_{2}=6$

Plug the values into the formula and reduce:

$(\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})=(\frac{2+8}{2},\frac{8+6}{2})=(5,7)$

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Question

Find the midpoint between and .

Answer

Write the formula for the midpoint.

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

Substitute the point into the formula.

$M = (\frac{-1+3}{2},\frac{-3+(-1)}{2} ) = (1,-2)$

The answer is:

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Question

What is the coordinates of the point exactly half way between (-2, -3) and (5, 7)?

Answer

We need to use the midpoint formula to solve this question.

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

In our case

and

Therefore, substituting these values in we get the following:

$midpoint=(\frac{-2+5}{2}, \frac{-3+7}{2})$

$midpoint= (\frac{3}{2}, \frac{4}{2})$

$(\frac{3}{2}, 2)$

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Question

Find the point halfway between points A and B.

Answer

Find the point halfway between points A and B.

We are going to need to use midpoint formula. If you ever have difficulty recalling midpoint formula, try to recall that it is basically taking two averages. One average is the average of your x values, the other average is the average of your y values.

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

Now we plug and chug!

$Mid=(\frac{19+67}{2},\frac{54+34}{2})=(\frac{86}{2},\frac{88}{2})=(43,44)$

So our answer is (43,44)

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Question

Find the midpoint between and .

Answer

Write the midpoint formula.

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

Substitute the points.

$M = (\frac{2+(-1)}{2}, \frac{3+9}{2}) = (\frac{1}{2}, 6)$

The answer is: $(\frac{1}{2}, 6)$

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Question

What is the midpoint of the points (3,12) and (9,15)?

Answer

To find the midpoint we must know the midpoint formula which is

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

We then take the -coordinate from the first point and plug it into the formula as $x_{1}$ .

We take the -coordinate from the second point and plug it into the formula as $x_{2}$ .

We then do the same for $y_{1}$ and $y_{2}$ .

With all of the points plugged in our equation will look like this.

$(\frac{3+9}{2},\frac{12+15}{2})$

We then perform the necessary addition and division to get the answer of

$(\frac{12}{2},\frac{27}{2})=(6,13.5)$

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Question

Find the midpoint of the line segment that connects the two points below.

Point 1:

Point 2:

Answer

The average of the the -coordinates and the average of the y-coordinates of the given points will give you the mid-point of the line that connects the points.

$\textup{midpoint}=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$ , where is and is .

$(\frac{(0)+(-2)}{2}, \frac{(-3)+(4)}{2})$

$(\frac{-2}{2},\frac{1}{2})$

$(-1, \frac{1}{2})$

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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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Question

What is the midpoint between $\left ( 2,3\right )$ and $\left ( -7,4\right )$ ?

Answer

The formula to find the midpoint is as follows:

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

In our case our

our

substituting in these values we get

midpoint = $\left(\frac{2+-7}{2}, \frac{3+4}{2}\right)=\left(\frac{-5}{2}, \frac{7}{2}\right)$

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