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SSAT Upper Level Math : Geometry

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

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All SSAT Upper Level Math Resources

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Example Questions

Example Question #1 : How To Find The Slope Of A Perpendicular Line

What is the slope of the line perpendicular to the line given by the equation

6x – 9y +14 = 0

Possible Answers:

-1/6

-3/2

-2/3

2/3

Correct answer:

-3/2

Explanation:

First rearrange the equation so that it is in slope-intercept form, resulting in y=2/3 x + 14/9. The slope of this line is 2/3, so the slope of the line perpendicular will have the opposite reciprocal as a slope, which is -3/2.

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Example Question #1 : How To Find The Slope Of A Perpendicular Line

What is the slope of the line perpendicular to the line represented by the equation y = -2x+3?

Possible Answers:

-1/2

2/3

1/2

-2/3

Correct answer:

1/2

Explanation:

Perpendicular lines have slopes that are the opposite of the reciprocal of each other. In this case, the slope of the first line is -2. The reciprocal of -2 is -1/2, so the opposite of the reciprocal is therefore 1/2.

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Example Question #2 : How To Find The Slope Of A Perpendicular Line

Find the slope of a line perpendicular to the line y = –3x – 4.

Possible Answers:

1/4

–3

1/3

Correct answer:

1/3

Explanation:

First we must find the slope of the given line. The slope of y = –3x – 4 is –3. The slope of the perpendicular line is the negative reciprocal. This means you change the sign of the slope to its opposite: in this case to 3. Then find the reciprocal by switching the denominator and numerator to get 1/3; therefore the slope of the perpendicular line is 1/3.

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Example Question #1 : How To Find The Slope Of A Perpendicular Line

What is the slope of a line perpendicular to the following:

$y-3=\frac{1}{2}(x-4)$

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{2}$

Correct answer:

Explanation:

The question puts the line in point-slope form y – y₁ = m(x – x₁), where m is the slope. Therefore, the slope of the original line is 1/2. A line perpendicular to another has a slope that is the negative reciprocal of the slope of the other line. The negative reciprocal of the original line is –2, and is thus the slope of its perpendicular line.

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Example Question #1 : How To Find The Slope Of A Perpendicular Line

A line is defined by the following equation:

2x-4y=6

What is the slope of a line that is perpendicular to the line above?

Possible Answers:

$\frac{1}{2}$

$-\frac{1}{2}$

Correct answer:

Explanation:

The equation of a line is y=mx+b where is the slope.

Rearrange the equation to match this:

2x-4y=6

-4y=-2x+6

4y=2x-6

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

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

$m=\frac{1}{2}$

For the perpendicular line, the slope is the negative reciprocal;

therefore $m=\frac{-2}{1}=-2$

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Example Question #71 : Coordinate Geometry

Find the slope of the line perpendicular to the line that has the equation y=2x-1 .

Possible Answers:

$\frac{1}{2}$

$-\frac{1}{2}$

Correct answer:

$-\frac{1}{2}$

Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, change the sign and flip the fraction around.

$\frac{2}{1}\rightarrow-\frac{1}{2}$

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Example Question #72 : Coordinate Geometry

Find the slope of a line perpendicular to the line with the equation y=-9x-1 .

Possible Answers:

$\frac{1}{9}$

$-\frac{1}{9}$

Correct answer:

$\frac{1}{9}$

Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, change the sign and flip the fraction around to find the slope of the line perpendicular to the given one.

$-9\rightarrow\frac{1}{9}$

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Example Question #73 : Coordinate Geometry

Find the slope of a line that is perpendicular to the line with the equation $y=\frac{1}{5}x-2$ .

Possible Answers:

$-\frac{1}{5}$

$\frac{1}{5}$

Correct answer:

Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, change the sign and flip the fraction around to find the slope of the line perpendicular to the given one.

$\frac{1}{5}\rightarrow-5$

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Example Question #74 : Coordinate Geometry

Find the slope of a line that is perpendicular to the line with the equation $y=\frac{3}{2}x-1$ .

Possible Answers:

$-\frac{3}{2}$

$\frac{3}{2}$

$-\frac{2}{3}$

$\frac{2}{3}$

Correct answer:

$-\frac{2}{3}$

Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, change the sign and flip the fraction around to find the slope of the line perpendicular to the given one.

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

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Example Question #75 : Coordinate Geometry

Find the slope of a line that is perpendicular to the line with the equation $y=\frac{7}{6}x-8$ .

Possible Answers:

$-\frac{6}{7}$

$\frac{6}{7}$

$-\frac{7}{6}$

$\frac{7}{6}$

Correct answer:

$-\frac{6}{7}$

Explanation:

Perpendicular lines have slopes that are negative reciprocals of each other. In other words, change the sign and flip the fraction around to find the slope of the line perpendicular to the given one.

$\frac{7}{6}\rightarrow-\frac{6}{7}$

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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 #1 : How To Find The Slope Of A Perpendicular Line

Example Question #1 : How To Find The Slope Of A Perpendicular Line

Example Question #2 : How To Find The Slope Of A Perpendicular Line

Example Question #1 : How To Find The Slope Of A Perpendicular Line

Example Question #1 : How To Find The Slope Of A Perpendicular Line

Example Question #71 : Coordinate Geometry

Example Question #72 : Coordinate Geometry

Example Question #73 : Coordinate Geometry

Example Question #74 : Coordinate Geometry

Example Question #75 : Coordinate Geometry

All SSAT Upper Level Math Resources

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