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GED Math : Midpoint Formula

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Example Question #1 : Midpoint Formula

Find the midpoint of the line segment that connects the following points:

$\small (-5,-3)\ and\ (3,7)$

Possible Answers:

$\small (-1,2)$

$\small (1,2)$

$\small (-4,-5)$

$\small (4,5)$

Correct answer:

$\small (-1,2)$

Explanation:

Use the midpoint formula:

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

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

$\small mid=(\frac{-2}{2},\frac{4}{2})$

$\small mid=(-1,2)$

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Example Question #1 : Midpoint Formula

You are given A (3,7) and B(7, -1) . is the midpoint of $\overline{AC}$ ; is the midpoint of $\overline{AD}$ . What are the coordinates of ?

Possible Answers:

(-11, 31)

(6,1)

(4,5)

(19, -25)

Correct answer:

(19, -25)

Explanation:

Repeated application of the midpoint formula $\left (\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2} \right )$ yields the following:

Since is the midpoint of $\overline{AC}$ , substitute the coordinates of for $x_{1}$ and $y_{1}$ , set equal to the coordinates of , and solve as follows:

$7 = \frac{3+x_{2}}{2}$

$14 =3+x_{2}$

$x_{2} = 11$

$-1= \frac{7+y_{2}}{2}$

$-2= 7+y_{2}$

$-9= y_{2}$

is the point (11, -9) .

We can find the coordinates of similarly using those of and :

$11= \frac{3+x_{2}}{2}$

$22 = 3+x_{2}$

$19= x_{2}$

$-9= \frac{7+y_{2}}{2}$

$-18= 7+y_{2}$

$-25= y_{2}$

is the point (19, -25)

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Example Question #811 : Geometry And Graphs

You are given points A (8, 1) and D (1,9) . is the midpoint of $\overline{AD}$ , is the midpoint of $\overline{AC}$ , and is the midpoint of $\overline{BD}$ . Give the coordinates of .

Possible Answers:

(2.125,8)

(3.625, 6)

$\left ( 7.625, 2\right )$

(5.375, 4)

Correct answer:

(3.625, 6)

Explanation:

Repeated application of the midpoint formula, $\left (\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2} \right )$ , yields the following:

is the point (8,1) and is the point $\left (1, 9 \right )$ . is the midpoint of $\overline{AD}$ , so has coordinates

$\left (\frac{8+1}{2}, \frac{1+9}{2} \right )$ , or $\left ( 4.5, 5\right )$ .

is the midpoint of $\overline{AC}$ , so has coordinates

$\left (\frac{8+4.5}{2}, \frac{1+5}{2} \right )$ , or (6.25, 3) .

is the midpoint of $\overline{BD}$ , so has coordinates

$\left (\frac{6.25+1}{2}, \frac{3+9}{2} \right )$ , or (3.625, 6) .

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Example Question #4 : Midpoint Formula

What is the midpoint between (2,6) and (1 ,-9) ?

Possible Answers:

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

$(\frac{1}{2}, -\frac{15}{2})$

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

$(-\frac{1}{2}, -\frac{15}{2})$

$(\frac{3}{2}, -\frac{15}{2})$

Correct answer:

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

Explanation:

Write the formula to find the midpoint.

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

Substitute the points into the equation.

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

The midpoint is located at: $(\frac{3}{2}, -\frac{3}{2})$

The answer is: $(\frac{3}{2}, -\frac{3}{2})$

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Example Question #1 : Midpoint Formula

Find the midpoint of (1,7) and (-2,-6) .

Possible Answers:

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

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

$(-\frac{3}{2}, \frac{13}{2})$

(-1,1)

(3,13)

Correct answer:

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

Explanation:

Write the formula for the midpoint.

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

Substitute the points.

$M=(\frac{1+(-2)}{2},\frac{7+(-6)}{2}) = (\frac{-1}{2}, \frac{1}{2})$

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

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Example Question #1 : Midpoint Formula

What is the midpoint between (4,5) and (-7,10) ?

Possible Answers:

(11,15)

(-1.5,7.5)

(5.5,15)

(5.5,7.5)

(-3,15)

Correct answer:

(-1.5,7.5)

Explanation:

Recall that the general formula for the midpoint between two points is:

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

Think of this like being the "average" of your two points.

Based on your data, you know that your midpoint could be calculated as follows:

$(\frac{4-7}{2},\frac{5+10}{2})=(\frac{-3}{2},\frac{15}{2})$

This is the same as:

(-1.5,7.5)

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Example Question #1 : Midpoint Formula

What is the midpoint between the points (-10,4) and (-22,-4) ?

Possible Answers:

(-16,-4)

(-32,-8)

(-16,0)

(16,8)

(-32,0)

Correct answer:

(-16,0)

Explanation:

Recall that the general formula for the midpoint between two points is:

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

Think of this like being the "average" of your two points.

Based on your data, you know that your midpoint could be calculated as follows:

$(\frac{-10-22}{2},\frac{4-4}{2})=(\frac{-32}{2},\frac{0}{2})$

This is the same as:

(-16,0)

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Example Question #8 : Midpoint Formula

(0,5) is the midpoint between (84,1) and some other point. What is that point?

Possible Answers:

(-84,10)

(84,10)

(-42,4)

(-84,9)

(42,4)

Correct answer:

(-84,9)

Explanation:

Recall that the general formula for the midpoint between two points is:

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

Think of this like being the "average" of your two points.

Now, you can write your data out as follows, as you know the midpoint value as well as one of the values for your end points:

$(0,5)=(\frac{84+x_2}{2},\frac{1+y_2}{2})$

To finish solving, think of it like two different equations:

$\frac{84+x_2}{2}=0$

and

$\frac{1+y_2}{2}=5$

Now, solve each for the respective values:

84+x_2=0

x_2=-84

and

1+y_2=10

y_2=9

Therefore, your other point is (x_2,y_2) or (-84,9)

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Example Question #1 : Midpoint Formula

(-10,-22) is the midpoint between (-2,-7) and some other point. What is that point?

Possible Answers:

(-16,-25)

(-18,-44)

(-12,-29)

(-18,-37)

(-5,55)

Correct answer:

(-18,-37)

Explanation:

Recall that the general formula for the midpoint between two points is:

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

Think of this like being the "average" of your two points.

Now, you can write your data out as follows, as you know the midpoint value as well as one of the values for your end points:

$(-10,-22)=(\frac{-2+x_2}{2},\frac{-7+y_2}{2})$

To finish solving, think of it like two different equations:

$\frac{-2+x_2}{2}=-10$

and

$\frac{-7+y_2}{2}=-22$

Now, solve each for the respective values:

-2+x_2=-20

x_2=-18

and

-7+y_2=-44

y_2=-37

Therefore, your other point is (x_2,y_2) or (-18,-37)

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Example Question #10 : Midpoint Formula

Find the midpoint of the following points:

(8,2)

(10,4)

Possible Answers:

(10,3)

(9,3)

(2,2)

(18,6)

(9,4)

Correct answer:

(9,3)

Explanation:

To find the midpoint between two points, we will use the following formula:

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

where (x_1,x_2) and (y_1,y_2) are the given points.

So, given the points

(8,2) and (10,4) , we can substitute into the formula. We get

$M = (\frac{8+10}{2}, \frac{2+4}{2})$

$M = (\frac{18}{2}, \frac{6}{2})$

M = (9,3)

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GED Math : Midpoint Formula

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #1 : Midpoint Formula

Example Question #1 : Midpoint Formula

Example Question #811 : Geometry And Graphs

Example Question #4 : Midpoint Formula

Example Question #1 : Midpoint Formula

Example Question #1 : Midpoint Formula

Example Question #1 : Midpoint Formula

Example Question #8 : Midpoint Formula

Example Question #1 : Midpoint Formula

Example Question #10 : Midpoint Formula

All GED Math Resources

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