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GED Math : Geometry and Graphs

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Example Questions

Example Question #116 : 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:

(2, -6)

(3, -5)

(-5, 3)

(-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 #113 : 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:

(20, 21)

(19, -21)

(-19, -21)

(9, -10)

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 #121 : Coordinate Geometry

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

Possible Answers:

(1,4)

(3,7)

(7,3)

(5,5)

(4,6)

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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Example Question #21 : Midpoint Formula

Find the midpoint of the line connecting and .

Possible Answers:

(202,24)

(202,41)

(211,41)

(222,42)

Correct answer:

(211,41)

Explanation:

Find the midpoint of the line connecting and .

To find the midpoint, we will essentially average out our x and y values independently.

What this will look like is:

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

So, all we need to do is find the average of each of our dimensions and we are set.

$(x_m,y_m)=(\frac{9+413}{2},\frac{17+65}{2})=(\frac{422}{2},\frac{82}{2})=(211,41)$

So, our answer is:

(211,41)

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Example Question #22 : Midpoint Formula

A line with endpoints (1, 4) and (a, b) has a midpoint at (5, 12) . What is the value of a+b ?

Possible Answers:

Correct answer:

Explanation:

Recall how to find the midpoint of a segment:

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

Solve for :

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

a+1=10

a=9

Solve for :

$\frac{b+4}{2}=12$

b+4=24

b=20

Thus, a+b=9+20=29

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Example Question #23 : Midpoint Formula

Find the midpoint of the line connecting the following points.

(19,47) (99,123)

Possible Answers:

(89,58)

(40,38)

(55,89)

(59,85)

Correct answer:

(59,85)

Explanation:

Find the midpoint of the line connecting the following points.

(19,47) (99,123)

To find the midpoint, we will use midpoint formula, which essentially averages out the x and y values of our points.

Midpoint formula:

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

Now, plug in our points and solve!

$(x_m,y_m)=(\frac{19+99}{2}, \frac{47+123}{2})=(\frac{118}{2},\frac{170}{2})=(59,85)$

So, we have our answer:

(59,85)

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Example Question #24 : Midpoint Formula

Find the midpoint of a line segment that has endpoints at (-7, 5) and (10, -2) .

Possible Answers:

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

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

$(\frac{17}{2}, \frac{3}{2})$

$(\frac{15}{2}, \frac{17}{2})$

Correct answer:

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

Explanation:

Recall how to find the midpoint of a line:

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

Plug in the given points to find the midpoint.

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

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Example Question #831 : Geometry And Graphs

Use the distance formula to calculate the distance between the points $\small \small (4,2)$ and $\small (-7,3)$ .

Possible Answers:

$\small \sqrt{10}$

$\small \sqrt{34}$

$\small \sqrt{122}$

$\small 2\sqrt2$

Correct answer:

$\small \sqrt{122}$

Explanation:

The distance between 2 points can be determined using the distance formula:

$\small D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$\small D=\sqrt{(4-(-7))^2+(2-3)^2}$

$\small D=\sqrt{(11)^2+(-1)^2}$

$\small D=\sqrt{121+1}=\sqrt{122}$

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Example Question #832 : Geometry And Graphs

Provide your answer in its most simplified form.

Find the distance between the following two points: (7,0), (-3,5)

Possible Answers:

$\sqrt{153}$

$\sqrt{113}$

$\sqrt{125}$

$\sqrt{51}$

$5\sqrt{5}$

Correct answer:

$5\sqrt{5}$

Explanation:

To find the distance we need to use the distance formula:

$d = \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}$

Plug in your x and y values to get:

$d = \sqrt{(7 - (-3))^{2} + (0 - 5)^{2}}$

Combine like terms to get:

$d = \sqrt{(10)^{2} + (-5)^{2}}$

Continue with your order of operations:

$d = \sqrt{100 + 25}$

$d = \sqrt{125}$

Don't forget to simplify if possible:

$d = 5\sqrt{5}$

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Example Question #3 : Distance Formula

Provide your answer in its most simplified form.

Find the distance between these two points: (-10,-4), (3,8)

Possible Answers:

$\sqrt{313}$

$\sqrt{-313}$

$\sqrt{65}$

$\sqrt{193}$

$\sqrt{33}$

Correct answer:

$\sqrt{313}$

Explanation:

For this problem we must use the distance formula:

$d = \sqrt{(x_{1} - x_{2})^{2} + (y_{1} - y_{2})^{2}}$

Plug in your x and y values:

$d = \sqrt{((-10) - 3)^{2} + ((-4) - 8)^{2}}$

Combine like terms:

$d = \sqrt{(-13)^{2} + (-12)^{2}}$

Continue your order of operations:

$d = \sqrt{169 +144}$

$d = \sqrt{313}$

This cannot be simplified so you are left with the correct answer.

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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 #116 : Coordinate Geometry

Example Question #113 : Coordinate Geometry

Example Question #121 : Coordinate Geometry

Example Question #21 : Midpoint Formula

Example Question #22 : Midpoint Formula

Example Question #23 : Midpoint Formula

Example Question #24 : Midpoint Formula

Example Question #831 : Geometry And Graphs

Example Question #832 : Geometry And Graphs

Example Question #3 : Distance Formula

All GED Math Resources

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