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GED Math : Geometry and Graphs

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Example Questions

Example Question #43 : Parallel And Perpendicular Lines

The line 4y-8x=20 is graphed on a coordinate plane. Which of the following lines will be parallel to it?

Possible Answers:

$y=-\frac{1}{2}x+13$

$y=\frac{1}{2}x-7$

y=2x

y=-2x+4

y=-2x-5

Correct answer:

y=2x

Explanation:

When determining if one line is perpendicular or parallel to another, it's important to observe the slopes of the lines. Lines are parallel if they share the same slope. They must have the same "m" value. This can be easily assessed as long as the lines are in y=mx+b form. Lines will be perpendicular if the product of the two slopes equals . This means that the m values will be the negative inverse of each other when comparing two line equations.

For this problem, the first step is to rewrite the graphed equation so it is in y=mx+b form. Just keep in mind that what you do to one side, you must do to the other.

4y-8x=20

$4y-8x{\color{Blue} +8x}=20{\color{Blue} +8x}$

4y=8x+20

$\frac{4y}{4}=\frac{8x}{4}+\frac{20}{4}$

y=2x+5

Now we know that the slope of the graphed equation is m=2 . This means that for another line to be parallel, the second line must also have a slope of .

The only provided option is y=2x . The y-intercept does not matter.

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Example Question #44 : Parallel And Perpendicular Lines

The line 4y-8x=20 is graphed on a coordinate plane. Which of the following lines will be perpendicular to it?

Possible Answers:

$y=\frac{1}{2}x+15$

y=-2x

y={2}x+3

y=-{2}x+2

$y=-\frac{1}{2}x+7$

Correct answer:

$y=-\frac{1}{2}x+7$

Explanation:

For this problem, the first step is to rewrite the graphed equation so it is in y=mx+b form. Just keep in mind that what you do to one side, you must do to the other.

4y-8x=20

$4y-8x{\color{Blue} +8x}=20{\color{Blue} +8x}$

4y=8x+20

$\frac{4y}{4}=\frac{8x}{4}+\frac{20}{4}$

y=2x+5

Now we know that the slope of the graphed equation is m=2 . This means that for another line to be perpendicular, the second line must have a slope of $-\frac{1}{2}$ .

The only provided option is $y=-\frac{1}{2}x+7$ . The y-intercept does not matter.

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Example Question #45 : Parallel And Perpendicular Lines

Which of the following is parallel to the line 4y-6x+2 ?

Possible Answers:

y={2}x+11

$y=\frac{3}{2}x+21$

$y=-\frac{3}{2}x+55$

$y=\frac{2}{3}x+8$

y={3}x+1

Correct answer:

$y=\frac{3}{2}x+21$

Explanation:

For this problem, the first step is to rewrite the graphed equation so it is in y=mx+b form. Just keep in mind that what you do to one side, you must do to the other.

4y-6x+2

$4y-6x{\color{Blue} +6x}=2{\color{Blue} +6x}$

4y=6x+2

$\frac{4y}{4}=\frac{6x}{4}+\frac{2}{4}$

$y=\frac{3}{2}x+\frac{1}{2}$

Now we know that the slope of the graphed equation is $m=\frac{3}{2}$ . This means that for another line to be parallel, the second line must have the same slope.

The only provided option is $y=\frac{3}{2}x+21$ . The y-intercept does not matter.

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Example Question #811 : Geometry And Graphs

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

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

Possible Answers:

$\small (-4,-5)$

$\small (-1,2)$

$\small (1,2)$

$\small (4,5)$

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 #812 : Geometry And Graphs

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:

(19, -25)

(6,1)

(-11, 31)

(4,5)

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 #3 : Midpoint Formula

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:

(3.625, 6)

(2.125,8)

(5.375, 4)

$\left ( 7.625, 2\right )$

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 #3 : Midpoint Formula

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

Possible Answers:

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

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

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

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

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

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 #4 : Midpoint Formula

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

Possible Answers:

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

(-1,1)

(3,13)

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

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

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 #3 : Midpoint Formula

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

Possible Answers:

(5.5,7.5)

(11,15)

(5.5,15)

(-1.5,7.5)

(-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 #3 : Midpoint Formula

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

Possible Answers:

(-32,-8)

(-32,0)

(16,8)

(-16,0)

(-16,-4)

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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GED Math : Geometry and Graphs

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #43 : Parallel And Perpendicular Lines

Example Question #44 : Parallel And Perpendicular Lines

Example Question #45 : Parallel And Perpendicular Lines

Example Question #811 : Geometry And Graphs

Example Question #812 : Geometry And Graphs

Example Question #3 : Midpoint Formula

Example Question #3 : Midpoint Formula

Example Question #4 : Midpoint Formula

Example Question #3 : Midpoint Formula

Example Question #3 : Midpoint Formula

All GED Math Resources

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