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GED Math : Geometry and Graphs

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #5 : Midpoint Formula

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

Possible Answers:

(42,4)

(-84,9)

(-84,10)

(-42,4)

(84,10)

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 #6 : Midpoint Formula

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

Possible Answers:

(-5,55)

(-16,-25)

(-18,-37)

(-18,-44)

(-12,-29)

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 #5 : Midpoint Formula

Find the midpoint of the following points:

(8,2)

(10,4)

Possible Answers:

(9,4)

(9,3)

(10,3)

(2,2)

(18,6)

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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Example Question #821 : Geometry And Graphs

Find the midpoint given the following points:

(9,1) and (1, 2)

Possible Answers:

(5, 1.5)

(8, 1.5)

(8,1)

(5,2)

(10,3)

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 #1791 : Ged Math

Find the point halfway between the two following points:

(12,34) (18,64)

Possible Answers:

(14,48)

(-15,49)

(49,15)

(15,49)

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 #112 : Coordinate Geometry

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 #821 : Geometry And Graphs

Find the point midway between the following two points.

(99,45) (54,32)

Possible Answers:

(38.5,76.5)

(76.5,38.5)

(67.5,24.5)

(46.2,45,5)

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 #114 : Coordinate Geometry

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:

(6, 18)

(1.5, 4.5)

(-3, -9 )

(9, 3)

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 #111 : Coordinate Geometry

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

Possible Answers:

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

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

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

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

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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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #5 : Midpoint Formula

Example Question #6 : Midpoint Formula

Example Question #5 : Midpoint Formula

Example Question #821 : Geometry And Graphs

Example Question #822 : Geometry And Graphs

Example Question #1791 : Ged Math

Example Question #112 : Coordinate Geometry

Example Question #821 : Geometry And Graphs

Example Question #114 : Coordinate Geometry

Example Question #111 : Coordinate Geometry

All GED Math Resources

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