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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

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

Example Questions

Example Question #4 : How To Find Slope Of A Line

Find the slope of the line that passes through the points $(-6, 2)\text{ and }(4,-4)$ $\displaystyle (-6, 2)\text{ and }(4,-4)$

Possible Answers:

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

$\displaystyle -5$

$-\frac{3}{5}$ $\displaystyle -\frac{3}{5}$

$\displaystyle 5$

Correct answer:

$-\frac{3}{5}$ $\displaystyle -\frac{3}{5}$

Explanation:

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$ $\displaystyle \text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{-4-2}{4-(-6)}=\frac{-6}{10}=-\frac{3}{5}$ $\displaystyle \text{Slope}=\frac{-4-2}{4-(-6)}=\frac{-6}{10}=-\frac{3}{5}$

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Example Question #5 : How To Find Slope Of A Line

Find the slope of the line that passes through the points $(1,1)\text{ and }(-8,6)$ $\displaystyle (1,1)\text{ and }(-8,6)$ .

Possible Answers:

$-\frac{5}{9}$ $\displaystyle -\frac{5}{9}$

$\frac{9}{5}$ $\displaystyle \frac{9}{5}$

$\frac{5}{9}$ $\displaystyle \frac{5}{9}$

$-\frac{9}{5}$ $\displaystyle -\frac{9}{5}$

Correct answer:

$-\frac{5}{9}$ $\displaystyle -\frac{5}{9}$

Explanation:

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$ $\displaystyle \text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{6-1}{-8-1}=-\frac{5}{9}$ $\displaystyle \text{Slope}=\frac{6-1}{-8-1}=-\frac{5}{9}$

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Example Question #6 : How To Find Slope Of A Line

Find the slope of the line that passes through the points $(2, -3)\text{ and }(-3, -3)$ $\displaystyle (2, -3)\text{ and }(-3, -3)$

Possible Answers:

$\text{Undefined}$ $\displaystyle \text{Undefined}$

$\frac{5}{6}$ $\displaystyle \frac{5}{6}$

$\frac{6}{5}$ $\displaystyle \frac{6}{5}$

$\displaystyle 0$

Correct answer:

$\displaystyle 0$

Explanation:

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$ $\displaystyle \text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{-3-(-3)}{-3-2}=\frac{0}{-5}=0$ $\displaystyle \text{Slope}=\frac{-3-(-3)}{-3-2}=\frac{0}{-5}=0$

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Example Question #302 : Ssat Upper Level Quantitative (Math)

Find the slope of the line that passes through the points $\left(\frac{1}{3}, -\frac{4}{5}\right)$ $\displaystyle \left(\frac{1}{3}, -\frac{4}{5}\right)$ and $\left ( -6,10\right )$ $\displaystyle \left ( -6,10\right )$ .

Possible Answers:

$\frac{162}{95}$ $\displaystyle \frac{162}{95}$

$-\frac{95}{162}$ $\displaystyle -\frac{95}{162}$

$\frac{95}{162}$ $\displaystyle \frac{95}{162}$

$-\frac{162}{95}$ $\displaystyle -\frac{162}{95}$

Correct answer:

$-\frac{162}{95}$ $\displaystyle -\frac{162}{95}$

Explanation:

Use the following formula to find the slope:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$ $\displaystyle \text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

Plug in the given points to find the slope.

$\text{Slope}=\frac{10-(-\frac{4}{5})}{-6-\frac{1}{3}}=\frac{\frac{54}{5}}{-\frac{19}{3}}=-\frac{162}{95}$ $\displaystyle \text{Slope}=\frac{10-(-\frac{4}{5})}{-6-\frac{1}{3}}=\frac{\frac{54}{5}}{-\frac{19}{3}}=-\frac{162}{95}$

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Example Question #7 : How To Find Slope Of A Line

A line goes passes through the points $\left(-\frac{1}{2}, 5\right)\text{ and }\left(\frac{3}{2}, -1\right)$ $\displaystyle \left(-\frac{1}{2}, 5\right)\text{ and }\left(\frac{3}{2}, -1\right)$ . What is the slope of this line?

Possible Answers:

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

$\displaystyle 3$

$\displaystyle -3$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

Correct answer:

$\displaystyle -3$

Explanation:

Use the following formula to find the slope of a line:

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$ $\displaystyle \text{Slope}=\frac{y_2-y_1}{x_2-x_1}$

The slope of this line would be

$\frac{-1-5}{\frac{3}{2}-(-\frac{1}{2})}=\frac{-6}{2}=-3$ $\displaystyle \frac{-1-5}{\frac{3}{2}-(-\frac{1}{2})}=\frac{-6}{2}=-3$

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Example Question #1 : Other Lines

What is the slope of line 3 = 8y - 4x?

Possible Answers:

0.5

-2

-0.5

Correct answer:

0.5

Explanation:

Solve equation for y. y=mx+b, where m is the slope

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

Find the slope of the line 6X – 2Y = 14

Possible Answers:

-6

-3

Correct answer:

Explanation:

Put the equation in slope-intercept form:

y = mx + b

-2y = -6x +14

y = 3x – 7

The slope of the line is represented by M; therefore the slope of the line is 3.

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

If 2x – 4y = 10, what is the slope of the line?

Possible Answers:

0.5

–0.5

–5/2

–2

Correct answer:

0.5

Explanation:

First put the equation into slope-intercept form, solving for y: 2x – 4y = 10 → –4y = –2x + 10 → y = 1/2*x – 5/2. So the slope is 1/2.

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Example Question #1411 : Gre Quantitative Reasoning

What is the slope of the line with equation 4x – 16y = 24?

Possible Answers:

1/2

–1/4

1/4

–1/8

1/8

Correct answer:

1/4

Explanation:

The equation of a line is:

y = mx + b, where m is the slope

4x – 16y = 24

–16y = –4x + 24

y = (–4x)/(–16) + 24/(–16)

y = (1/4)x – 1.5

Slope = 1/4

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Example Question #2 : Other Lines

What is the slope of a line which passes through coordinates $\dpi{100} \small (3,7)$ $\displaystyle \dpi{100} \small (3,7)$ and $\dpi{100} \small (4,12)$ $\displaystyle \dpi{100} \small (4,12)$ ?

Possible Answers:

$\dpi{100} \small 3$ $\displaystyle \dpi{100} \small 3$

$\dpi{100} \small 5$ $\displaystyle \dpi{100} \small 5$

$\dpi{100} \small \frac{1}{5}$ $\displaystyle \dpi{100} \small \frac{1}{5}$

$\dpi{100} \small \frac{1}{2}$ $\displaystyle \dpi{100} \small \frac{1}{2}$

$\dpi{100} \small 2$ $\displaystyle \dpi{100} \small 2$

Correct answer:

$\dpi{100} \small 5$ $\displaystyle \dpi{100} \small 5$

Explanation:

Slope is found by dividing the difference in the $\dpi{100} \small y$ $\displaystyle \dpi{100} \small y$ -coordinates by the difference in the $\dpi{100} \small x$ $\displaystyle \dpi{100} \small x$ -coordinates.

$\dpi{100} \small \frac{(12-7)}{(4-3)}=\frac{5}{1}=5$ $\displaystyle \dpi{100} \small \frac{(12-7)}{(4-3)}=\frac{5}{1}=5$

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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 Slope Of A Line

Example Question #5 : How To Find Slope Of A Line

Example Question #6 : How To Find Slope Of A Line

Example Question #302 : Ssat Upper Level Quantitative (Math)

Example Question #7 : How To Find Slope Of A Line

Example Question #1 : Other Lines

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

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

Example Question #1411 : Gre Quantitative Reasoning

Example Question #2 : Other Lines

All SSAT Upper Level Math Resources

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