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SSAT Upper Level Math : Geometry

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #4 : How To Find The Endpoints Of A Line Segment

One endpoint of a line segment on the coordinate plane is the point $\left (8.32, -4.29 \right )$ ; the midpoint of the segment is the point (-1.89, 8.56) . Give the -coordinate of the other endpoint of the segment.

Possible Answers:

-12.1

3.215

2.135

21.41

-12.85

Correct answer:

21.41

Explanation:

Using the part of the midpoint formula

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

set $y_{M}=8.56, y_{2}= -4.29$ and solve:

$8.56= \frac{y_{1} -4.29 }{2}$

$y_{1} -4.29 = 17.12$

$y_{1} = 21.41$

The second endpoint is ( -12.1, 21.41) .

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Example Question #4 : How To Find The Endpoints Of A Line Segment

On the coordinate plane, is the midpoint of $\overline{AB}$ and is the midpoint of $\overline{AM}$ . has coordinates (288, 108) and has coordinates $\left ( 176, 300\right )$ .

Give the -coordinate of .

Possible Answers:

102

876

156

Correct answer:

876

Explanation:

First, find the -coordinate of . In the part of the midpoint formula

$y_{M}= \frac{y_{1} + y_{2} }{2}$ ,

set $y_{M}=300, y_{2}= 108$ , and solve:

$300= \frac{y_{1} + 108}{2}$

$y_{1} + 108 = 600$

$y_{1} =492$

Now, find the -coordinate of similarly, setting

$y_{M}= 492,y_{2}= 108$

$492= \frac{y_{1} + 108}{2}$

$y_{1} + 108= 984$

$y_{1} = 876$

This is the correct response.

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Example Question #6 : How To Find The Endpoints Of A Line Segment

On the coordinate plane, is the midpoint of $\overline{AB}$ and is the midpoint of $\overline{AM}$ . has coordinates $\left (4\frac{1}{3},-12\frac{1}{2} \right )$ and has coordinates $\left ( -7 \frac{5}{6}, 6\frac{1}{3}\right )$ .

Give the -coordinate of .

Possible Answers:

$40\frac{5}{6}$

$62\frac{5}{6}$

$-44\frac{1}{3}$

$1\frac{1}{4}$

Correct answer:

$-44\frac{1}{3}$

Explanation:

First, find the -coordinate of . In the part of the midpoint formula

$x_{M}= \frac{x_{1} + x_{2} }{2}$ ,

set $x_{M}= -7 \frac{5}{6}, x_{2}= 4\frac{1}{3}$ , and solve:

$-7 \frac{5}{6}= \frac{x_{1} + 4\frac{1}{3}}{2}$

$x_{1} + 4\frac{1}{3}= -7 \frac{5}{6} \cdot 2$

$x_{1} + 4\frac{1}{3}= -15 \frac{2}{3}$

$x_{1} = -15 \frac{2}{3} - 4\frac{1}{3}$

$x_{1} = -20$

Now, find the -coordinate of similarly, setting

$x_{M}= -20, x_{2}= 4\frac{1}{3}$

$-20 = \frac{x_{1} + 4\frac{1}{3}}{2}$

$x_{1} + 4\frac{1}{3}= -20 \cdot 2$

$x_{1} + 4\frac{1}{3}= -40$

$x_{1} = -40 - 4\frac{1}{3}$

$x_{1} = -44\frac{1}{3}$

This is the correct response.

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Example Question #2 : How To Find The Endpoints Of A Line Segment

Give the -coordinate of .

Possible Answers:

$-44\frac{1}{3}$

$62\frac{5}{6}$

$-50\frac{1}{6}$

$37\frac{5}{6}$

$-24\frac{2}{3}$

Correct answer:

$62\frac{5}{6}$

Explanation:

First, find the -coordinate of . In the part of the midpoint formula

$y_{M}= \frac{y_{1} + y_{2} }{2}$ ,

set $y_{M}=6\frac{1}{3}, y_{2}= -12\frac{1}{2}$ , and solve:

$6\frac{1}{3}= \frac{y_{1} -12\frac{1}{2} }{2}$

$y_{1} -12\frac{1}{2}= 6\frac{1}{3} \cdot 2$

$y_{1} -12\frac{1}{2}=12 \frac{2}{3}$

$y_{1} =12 \frac{2}{3} + 12\frac{1}{2}$

$y_{1} = 25\frac{1}{6}$

Now, find the -coordinate of similarly, setting

$y_{M}=25\frac{1}{6}, y_{2}= -12\frac{1}{2}$

$25\frac{1}{6}= \frac{y_{1} -12\frac{1}{2} }{2}$

$y_{1} -12\frac{1}{2} = 25\frac{1}{6} \cdot 2$

$y_{1} -12\frac{1}{2} = 50\frac{1}{3}$

$y_{1} = 50\frac{1}{3} +12\frac{1}{2}$

$y_{1} = 62\frac{5}{6}$

This is the correct response.

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Example Question #3 : How To Find The Endpoints Of A Line Segment

On the coordinate plane, is the midpoint of $\overline{AB}$ and is the midpoint of $\overline{AM}$ . has coordinates (288, 108) and has coordinates $\left ( 176, 300\right )$ .

Give the -coordinate of .

Possible Answers:

684

736

204

116

Correct answer:

Explanation:

First, find the -coordinate of . In the part of the midpoint formula using the coordinates from and

$x_{M}= \frac{x_{1} + x_{2} }{2}$ ,

set $x_{M}= 176, x_{2}= 288$ , and solve:

$176= \frac{x_{1} + 288}{2}$

$x_{1} + 288 = 352$

$x_{1} =64$

Now, find the -coordinate of similarly, setting

$x_{M}= 64, x_{2}= 288$

$64= \frac{x_{1} + 288}{2}$

$x_{1} + 288 = 128$

$x_{1} = -160$

This is the correct response.

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Example Question #1 : Parallel Lines

Which of the following lines is parallel to y=9x-2 ?

Possible Answers:

$y=\frac{1}{9}x-8$

y=9x-8

$y=-\frac{1}{9}x-2$

y=-9x+2

Correct answer:

y=9x-8

Explanation:

Lines that are parallel must have the same slope. Thus, the correct answer must also have a slope of .

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Example Question #405 : Ssat Upper Level Quantitative (Math)

Which of the following lines is parallel to the line 2x-y=4 ?

Possible Answers:

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

$y=-\frac{1}{2}x-8$

y=-2x-1

y=2x-1

Correct answer:

y=2x-1

Explanation:

First, put the equation in the more familiar y=mx+b format to see what the slope of the given line is.

2x-y=4

y=2x-4

Lines that are parallel must have the same slope. Thus, the correct answer must also have a slope of .

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Example Question #411 : Ssat Upper Level Quantitative (Math)

Which of the following lines is parallel with the line $-4x+\frac{1}{2}y=8$ ?

Possible Answers:

y=-8x+7

y=4x-2

y=-4x-1

y=8x+6

Correct answer:

y=8x+6

Explanation:

First, put the given equation in the more familiar y=mx+b format to find out the slope of the given line.

$-4x+\frac{1}{2}y=8$

$\frac{1}{2}y=4x+8$

y=8x+16

Lines that are parallel must share the same slope. Thus, the line that is parallel has a slope of .

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Example Question #2 : Parallel Lines

Which of the following lines is parallel to the line y=6x-1 ?

Possible Answers:

y=-6x+1

$y=-\frac{1}{6}x+19$

$y=\frac{1}{6}x-9$

y=6x+19

Correct answer:

y=6x+19

Explanation:

Lines that are parallel have the same slope, so the correct answer must also have the slope of .

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Example Question #3 : Parallel Lines

Which of the following lines is parallel to the line y=-4x+12 ?

Possible Answers:

y=4x-1

y=-4x-2

$y=\frac{1}{4}x-2$

$y=-\frac{1}{4}x+2$

Correct answer:

y=-4x-2

Explanation:

For two lines to be parallel, their slopes must be the same. Thus, the line that is parallel to the given one must also have a slope of .

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Geometry

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #4 : How To Find The Endpoints Of A Line Segment

Example Question #4 : How To Find The Endpoints Of A Line Segment

Example Question #6 : How To Find The Endpoints Of A Line Segment

Example Question #2 : How To Find The Endpoints Of A Line Segment

Example Question #3 : How To Find The Endpoints Of A Line Segment

Example Question #1 : Parallel Lines

Example Question #405 : Ssat Upper Level Quantitative (Math)

Example Question #411 : Ssat Upper Level Quantitative (Math)

Example Question #2 : Parallel Lines

Example Question #3 : Parallel Lines

All SSAT Upper Level Math Resources

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