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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 #5 : How To Graph A Point

What are the coordinates for point F?

Graph6

Possible Answers:

(-4, -6)

(-6, -4)

(4, 6)

(-4, 6)

Correct answer:

(-4, -6)

Explanation:

Find the x-coordinate by going left on the horizontal x-axis until you come across the line that is directly above the point. The x-coordinate is .

Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is .

(-4, -6) are the coordinates for point F.

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Example Question #31 : Graphing

What are the coordinates for point G?

Graph7

Possible Answers:

(-2, -3)

(3, 2)

(-3, -2)

(2, 3)

Correct answer:

(2, 3)

Explanation:

Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is .

Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is .

(2, 3) are the coordinates for point G.

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Example Question #221 : Coordinate Plane

What are the coordinates for point H?

Graph8

Possible Answers:

(-6, 5)

(-6, -5)

(6, 5)

(5, 6)

Correct answer:

(6, 5)

Explanation:

Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is .

Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is .

(6, 5) are the coordinates for point H.

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Example Question #2 : How To Graph A Point

What are the coordinates for point J?

Graph9

Possible Answers:

(5, 0)

(-5, 0)

(0, -5)

(0, 5)

Correct answer:

(0, 5)

Explanation:

Since there is no movement on the x-axis, the x-coordinate is .

Go up the vertical y-axis until you reach the point. The y-coordinate is .

(0, 5) are the coordinates of point J.

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Example Question #3 : How To Graph A Point

What are the coordinates for point L?

Graph11

Possible Answers:

(2, -5)

(5, 2)

(2, 5)

(-5, 2)

Correct answer:

(2, -5)

Explanation:

Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly above the point. The x-coordinate is .

Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is .

(2, -5) are the coordinates for point L.

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Example Question #861 : Act Math

What are the coordinates for point M?

Graph12

Possible Answers:

(4, 7)

(7, 4)

(-4, 7)

(-7, -4)

Correct answer:

(7, 4)

Explanation:

Find the x-coordinate by going right on the horizontal x-axis until you come across the line that is directly under the point. The x-coordinate is .

Now, continue up until you reach the point and look across to the vertical y-axis. The y-coordinate is .

(7, 4) are the coordinates for point M.

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Example Question #221 : Algebra

What are the coordinates for point K?

Graph10

Possible Answers:

(6, 3)

(-6, 3)

(-6, -3)

(-3, -6)

Correct answer:

(-6, -3)

Explanation:

Find the x-coordinate by going left on the horizontal x-axis until you come across the line that is above the point. The x-coordinate is .

Now, continue down until you reach the point and look across to the vertical y-axis. The y-coordinate is .

(-6, -3) are the coordinates for point K.

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Example Question #1 : Graphing Linear Functions

Line

Refer to the above red line. A line is drawn perpendicular to that line, and with the same -intercept. Give the equation of that line in slope-intercept form.

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

First, we need to find the slope of the above line.

The slope of a line. given two points $(x_{1}, y_{1}), (x_{2}, y_{2})$ can be calculated using the slope formula

$m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $x_{1}=-4, y_{1}=x_{2}= 0, y_{2}=8$ :

$m = \frac{8-0}{0-(-4)} = \frac{8}{4} = 2$

The slope of a line perpendicular to it has as its slope the opposite of the reciprocal of 2, which would be $m = -\frac{1}{2}$ . Since we want this line to have the same -intercept as the first line, which is the point (0,8) , we can substitute $m = -\frac{1}{2}$ and b = 8 in the slope-intercept form:

y = mx + b

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

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Example Question #402 : Sat Subject Test In Math I

Axes

Refer to the above diagram. If the red line passes through the point $\left ( N, 4\right )$ , what is the value of ?

Possible Answers:

$N= -1\frac{1}{3}$

$N = -7\frac{1}{3}$

N = -5

$N = -4\frac{2}{3}$

$N = -3\frac{1}{3}$

Correct answer:

$N = -4\frac{2}{3}$

Explanation:

One way to answer this is to first find the equation of the line.

The slope of a line. given two points $(x_{1}, y_{1}), (x_{2}, y_{2})$ can be calculated using the slope formula

$m = \frac{y_{2}-y_{1}}{x_{2}-x _{1}}$

Set $x_{1}=-6, y_{1}=x_{2}= 0, y_{2}=18$ :

$m = \frac{18-0}{0-(-6)} = \frac{18}{6} = 3$

The line has slope 3 and -intercept (0,18) , so we can substitute m = 3, b = 18 in the slope-intercept form:

y = mx+b

y = 3x+18

Now substitute 4 for and for and solve for :

4= 3N+18

-14 =3N

$N = -\frac{14}{3}= -4\frac{2}{3}$

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Example Question #381 : Geometry

Multiply:

$\left (7 - 2i \right )\left (7 - 3i \right )$

Possible Answers:

43 -35i

55 -35i

55 +7i

43 -7i

49 + 6i

Correct answer:

43 -35i

Explanation:

FOIL the product out:

$\left (7 - 2i \right )\left (7 - 3i \right )$

$= 7 \cdot 7 - 7 \cdot 3i - 7 \cdot 2i + 2i \cdot 3i$

$= 49 -21i - 14i + 6 i^{2}$

= 49 -21i - 14i + 6 (-1)

= 49 -6 -21i - 14i

= 43 -35i

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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 #5 : How To Graph A Point

Example Question #31 : Graphing

Example Question #221 : Coordinate Plane

Example Question #2 : How To Graph A Point

Example Question #3 : How To Graph A Point

Example Question #861 : Act Math

Example Question #221 : Algebra

Example Question #1 : Graphing Linear Functions

Example Question #402 : Sat Subject Test In Math I

Example Question #381 : Geometry

All SSAT Upper Level Math Resources

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