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GED Math : Midpoint Formula

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Example Question #821 : Geometry And Graphs

Find the midpoint given the following points:

(9,1) and (1, 2)

Possible Answers:

(10,3)

(8, 1.5)

(5,2)

(5, 1.5)

(8,1)

Correct answer:

(5, 1.5)

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 (9,1) and (1, 2) , we can substitute. We get

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

$M = (\frac{10}{2}, \frac{3}{2})$

M = (5, 1.5)

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Example Question #822 : Geometry And Graphs

The midpoint of a line with endpoints at (3, 5) and (-5, y) is (-2, 12) . Find the value of .

Possible Answers:

Correct answer:

Explanation:

Recall how to find the midpoint of a line:

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

Since we are only worried about the -coordinate, we can write the following equation:

$\frac{5+y}{2}=12$

Solve for .

5+y=24

y=19

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Example Question #823 : Geometry And Graphs

Find the point halfway between the two following points:

(12,34) (18,64)

Possible Answers:

(15,49)

(49,15)

(-15,49)

(14,48)

Correct answer:

(15,49)

Explanation:

Find the point halfway between the two following points:

(12,34) (18,64)

We need to use the midpoint formula. To do so, we are basically averaging out our x and y values separately.

$x_{mid}=\frac{x_1+x_2}{2}$

$y_{mid}=\frac{y_1+y_2}{2}$

So, plug in our values to solve:

$x_{mid}=\frac{12+18}{2}=15$

$y_{mid}=\frac{34+64}{2}=49$

So, our answer is (15,49)

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Example Question #824 : Geometry And Graphs

If (4, 14) is the midpoint of a line that has endpoints at (-2, -2) and (10, y) , find the value of .

Possible Answers:

Correct answer:

Explanation:

Recall how to find the midpoint of a line when given two points:

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

Since the y-coordinate of the midpoint is , we can write the following equation:

$14=\frac{-2+y}{2}$

Solve for .

-2+y=28

y=30

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Example Question #11 : Midpoint Formula

Find the point midway between the following two points.

(99,45) (54,32)

Possible Answers:

(46.2,45,5)

(38.5,76.5)

(67.5,24.5)

(76.5,38.5)

Correct answer:

(38.5,76.5)

Explanation:

Find the point midway between the following two points.

(99,45) (54,32)

To find the midpoint, we need to essentially average our x and y values separately.

$x_m=\frac{x_1+x_2}{2}=\frac{54+99}{2}=\frac{153}{2}=76.5$

$y_m=\frac{y_1+y_2}{2}=\frac{45+32}{2}=\frac{77}{2}=38.5$

So, our answer is

(38.5,76.5)

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Example Question #12 : Midpoint Formula

The midpoint of a line segment on the coordinate plane is located at (3, 9) ; one endpoint is located at the origin. Where is the other endpoint?

Possible Answers:

(-3, -9 )

(1.5, 4.5)

(9, 3)

(6, 18)

Correct answer:

(6, 18)

Explanation:

The midpoint of a line segment with its endpoints at $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is at the point $(x_{M}, y_{M})$ , where

$x_{M} = \frac{ x_{1} + x_{2}}{2}$ and $y_{M} = \frac{ y_{1} + y_{2}}{2}$ .

The midpoint and one endpoint are given, so first, find the -coordinate of the second endpoint by setting $x_{M} =3$ and $x_{2} =0$ , and solving for $x_{1}$ :

$3 = \frac{ x_{1} +0}{2}$

$3 = \frac{ x_{1} }{2}$

Isolate $x_{1 }$ by multiplying both sides by 2:

$3 \cdot 2 = \frac{ x_{1} }{2} \cdot 2$

$6 = x_{1}$

Find the -coordinate of the second endpoint similarly, setting $y_{M} =9$ and $y_{2} =0$ :

$9 = \frac{ y_{1} +0}{2}$

$9 = \frac{ y_{1} }{2}$

$9 \cdot 2 = \frac{ y_{1} }{2} \cdot 2$

$18 = y_{1}$

The second endpoint of the segment is at (6, 18) .

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Example Question #11 : Midpoint Formula

A line on a coordinate graph has endpoints at (4, 5) and (-10, 2) . What is the midpoint of the line?

Possible Answers:

$(3, \frac{7}{2})$

$(-7, \frac{3}{2})$

$(-3, \frac{7}{2})$

$(3, -\frac{5}{2})$

Correct answer:

$(-3, \frac{7}{2})$

Explanation:

Recall how to find the midpoint of a line when given two endpoints:

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

Plug in the given points to find the midpoint.

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

The midpoint of the line is located at $(-3, \frac{7}{2})$ .

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Example Question #111 : Coordinate Geometry

The midpoint of a line that passes through the points (5, 1) and (x, y) is (4, -2) . Find the coordinates of the point (x, y) .

Possible Answers:

(3, -5)

(-5, 3)

(2, -6)

(-5, -3)

Correct answer:

(3, -5)

Explanation:

Recall how to find the midpoint of a line:

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

Start by finding the x-coordinate.

$\frac{5+x}{2}=4$

5+x=8

x=3

Next, find the y-coordinate.

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

1+y=-4

y=-5

The coordinates for the second endpoint is (3, -5)

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Example Question #111 : Coordinate Geometry

If the midpoint of a line with one endpoint at (5, 1) is (12, -10) , what are the coordinates for the other endpoint?

Possible Answers:

(9, -10)

(19, -21)

(20, 21)

(-19, -21)

Correct answer:

(19, -21)

Explanation:

Recall how to find the midpoint of a line segment:

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

Start by finding the x-coordinate of the other endpoint.

$12=\frac{5+x}{2}$

5+x=24

x=19

Next, find the y-coordinate of the other endpoint.

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

1+y=-20

y=-21

The other endpoint must be (19, -21) .

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Example Question #833 : Geometry And Graphs

The two endpoints of a line segment are (1,4) and (5,10) . Find the midpoint of the line segment.

Possible Answers:

(4,6)

(5,5)

(3,7)

(7,3)

(1,4)

Correct answer:

(3,7)

Explanation:

To find the midpoint of a line, you basically have to average the two values and average the two values. In other words, you have to add the two values and then divide by , and add the two values and then divide by . The standard equation for the midpoint formula is $((x_{1} + x_{2}) / 2, (y_{1} + y_{2}) / 2)$ .

The two values are and , and (1+5)/2=3 , so the coordinate of your midpoint is . The two values are and , and (4+10)/2 = 7 , so the coordinate of your midpoint is .

Therefore, the midpoint is (3,7) .

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GED Math : Midpoint Formula

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #821 : Geometry And Graphs

Example Question #822 : Geometry And Graphs

Example Question #823 : Geometry And Graphs

Example Question #824 : Geometry And Graphs

Example Question #11 : Midpoint Formula

Example Question #12 : Midpoint Formula

Example Question #11 : Midpoint Formula

Example Question #111 : Coordinate Geometry

Example Question #111 : Coordinate Geometry

Example Question #833 : Geometry And Graphs

All GED Math Resources

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