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SSAT Upper Level Math : Geometry

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All SSAT Upper Level Math Resources

6 Diagnostic Tests 311 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #131 : Geometry

Find the slope of a line that is perpendicular to the line with the equation $y=\frac{4}{5}x+9$ .

Possible Answers:

$-\frac{5}{4}$

$-\frac{4}{5}$

$\frac{5}{4}$

$\frac{4}{5}$

Correct answer:

$-\frac{5}{4}$

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.

$\frac{4}{5}\rightarrow-\frac{5}{4}$

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Example Question #132 : Geometry

Find the slope of a line that is perpendicular to the line with the equation $y=\frac{9}{4}x-5$ .

Possible Answers:

$\frac{9}{4}$

$\frac{4}{9}$

$-\frac{9}{4}$

$-\frac{4}{9}$

Correct answer:

$-\frac{4}{9}$

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.

$\frac{9}{4}\rightarrow-\frac{4}{9}$

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Example Question #133 : Geometry

Find the slope of a line that is perpendicular to the line with the equation $y=\frac{4}{5}x-8$ .

Possible Answers:

$-\frac{5}{4}$

$\frac{4}{5}$

$\frac{5}{4}$

$-\frac{4}{5}$

Correct answer:

$-\frac{5}{4}$

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.

$\frac{4}{5}\rightarrow-\frac{5}{4}$

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Example Question #79 : Coordinate Geometry

Find the slope of a line that is perpendicular to the line with the equation $y=-\frac{3}{8}x+2$ .

Possible Answers:

$\frac{8}{3}$

$-\frac{3}{8}$

$\frac{3}{8}$

$-\frac{8}{3}$

Correct answer:

$\frac{8}{3}$

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.

$-\frac{3}{8}\rightarrow\frac{8}{3}$

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Example Question #134 : Geometry

Find the slope of a line that is perpendicular to the line with the equation $y=\frac{2}{15}x+15$ .

Possible Answers:

$\frac{15}{2}$

$-\frac{15}{2}$

$\frac{2}{15}$

$-\frac{2}{15}$

Correct answer:

$-\frac{15}{2}$

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.

$\frac{2}{15}\rightarrow-\frac{15}{2}$

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Example Question #135 : Geometry

Find the slope of a line that is perpendicular to the line with the equation $y=-\frac{4}{19}x-8$ .

Possible Answers:

$\frac{19}{4}$

$-\frac{4}{19}$

$-\frac{19}{4}$

$\frac{4}{19}$

Correct answer:

$\frac{19}{4}$

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.

$-\frac{4}{19}\rightarrow\frac{19}{4}$

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Example Question #136 : Geometry

Find the slope of a line that is perpendicular to the line with the equation $y=\frac{9}{17}x-2$ .

Possible Answers:

$-\frac{17}{9}$

$-\frac{9}{17}$

$\frac{9}{17}$

$\frac{17}{9}$

Correct answer:

$-\frac{17}{9}$

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.

$\frac{9}{17}\rightarrow-\frac{17}{9}$

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

What line is perpendicular to x + 3y = 6 and travels through point (1,5)?

Possible Answers:

y = 2/3x + 6

y = 2x + 1

y = 3x + 2

y = –1/3x – 4

y = 6x – 3

Correct answer:

y = 3x + 2

Explanation:

Convert the equation to slope intercept form to get y = –1/3x + 2. The old slope is –1/3 and the new slope is 3. Perpendicular slopes must be opposite reciprocals of each other: m_{1 *}m₂ = –1

With the new slope, use the slope intercept form and the point to calculate the intercept: y = mx + b or 5 = 3(1) + b, so b = 2

So y = 3x + 2

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

What line is perpendicular to 3x + 5y = 15 and passes through (3,2) ?

Possible Answers:

$y = \frac{1}{3}x - 5$

$y = \frac{5}{3}x - 3$

$y = \frac{-3}{5}x + 2$

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

$y = \frac{2}{5}x + 4$

Correct answer:

$y = \frac{5}{3}x - 3$

Explanation:

Convert the given equation to slope-intercept form.

3x + 5y = 15

5y=-3x+15

$y=-\frac{3}{5}+3$

The slope of this line is $-\frac{3}{5}$ . The slope of the line perpendicular to this one will have a slope equal to the negative reciprocal.

The perpendicular slope is $\frac{5}{3}$ .

Plug the new slope and the given point into the slope-intercept form to find the y-intercept.

$2 = \frac{5}{3}(3) + b$

2=5+b

b = -3

So the equation of the perpendicular line is $y = \frac{5}{3}x - 3$ .

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

What is the equation of a line that runs perpendicular to the line 2x + y = 5 and passes through the point (2,7)?

Possible Answers:

–x/2 + y = 6

2x – y = 6

2x + y = 7

x/2 + y = 5

x/2 – y = 6

Correct answer:

–x/2 + y = 6

Explanation:

First, put the equation of the line given into slope-intercept form by solving for y. You get y = -2x +5, so the slope is –2. Perpendicular lines have opposite-reciprocal slopes, so the slope of the line we want to find is 1/2. Plugging in the point given into the equation y = 1/2x + b and solving for b, we get b = 6. Thus, the equation of the line is y = ½x + 6. Rearranged, it is –x/2 + y = 6.

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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 #131 : Geometry

Example Question #132 : Geometry

Example Question #133 : Geometry

Example Question #79 : Coordinate Geometry

Example Question #134 : Geometry

Example Question #135 : Geometry

Example Question #136 : Geometry

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

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

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

All SSAT Upper Level Math Resources

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