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SSAT Middle Level Math : Geometry

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Example Questions

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Example Question #5 : Graphing Points

Which of the following points is in Quadrant II on the coordinate plane?

Possible Answers:

(-4,0)

(-4,-5)

(-4,5)

(4,-5)

(4,5)

Correct answer:

(-4,5)

Explanation:

All points in Quadrant II have negative -coordinates and positive -coordinates. The only answer that fulfills these criteria is (-4,5) .

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Example Question #21 : Graphing

In which quadrant or on which axis will we find the point (7,0) ?

Possible Answers:

Quadrant I

Quadrant II

The -axis

Quadrant IV

Correct answer:

The -axis

Explanation:

By definition, any point in the coordinate plane that has a non-zero value -coordinate and a zero-value -coordinate is on the -axis.

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Example Question #22 : Graphing

In which quadrant or on which axis of the coordinate plane will you find the point (6,-9) ?

Possible Answers:

Quadrant III

Quadrant I

Quadrant II

The -axis

Quadrant IV

Correct answer:

Quadrant IV

Explanation:

A point with a positive -coordinate and a negative -coordinate can be found in Quadrant IV.

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Example Question #1 : How To Find The Points On A Coordinate Plane

A line segment on the coordinate plane has its endpoints at the points with coordinates $\left ( - 10, -20 \right )$ and $\left ( -20,10 \right )$ . Give the coordinates of the midpoint of the segment.

Possible Answers:

(-5, -15)

(-30, -10)

(-15, -5)

(-10, -30)

Correct answer:

(-15, -5)

Explanation:

The -coordinate of the midpoint can be found by dividing the sum of the -coordinates of the endpoints by 2:

$\left [(-10 ) + (-20) \right ] \div 2 = \left [-(10 + 20) \right ] \div 2 = -30 \div 2 = -15$

The -coordinate of the midpoint is found similarly:

$\left [ (-20)+ 10 \right ] \div 2 = \left [-(20-10) \right ] \div 2 = -10 \div 2 = -5$

The coordinates of the midpoint are (-15, -5) .

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Example Question #4 : How To Find The Points On A Coordinate Plane

A line segment on the coordinate plane has its endpoints at the points with coordinates $\left ( 4 \frac{1}{3}, - 4 \frac{1}{3}\right )$ and $\left ( 12, 12\right )$ . Give the coordinates of the midpoint of the segment.

Possible Answers:

$\left ( 3 \frac{5}{6} , 8 \frac{1}{6} \right )$

$\left ( 8 \frac{1}{6}, 3 \frac{5}{6} \right )$

$\left ( 16 \frac{1}{3}, 7 \frac{2}{3} \right )$

$\left ( 7 \frac{2}{3}, 16 \frac{1}{3}\right )$

Correct answer:

$\left ( 8 \frac{1}{6}, 3 \frac{5}{6} \right )$

Explanation:

The -coordinate of the midpoint is half the sum of the -coordinates of the endpoints:

$\frac{1}{2} \left ( 4 \frac{1}{3} + 12 \right )$

$= \frac{1}{2} \times 16 \frac{1}{3}$

$= \frac{1}{2} \times \frac{49}{3}$

$= \frac{49}{6}$

$=8 \frac{1}{6}$

The -coordinate of the midpoint is found similarly:

$\frac{1}{2} \left (- 4 \frac{1}{3} + 12 \right )$

$= \frac{1}{2} \left (12 - 4 \frac{1}{3} \right )$

$= \frac{1}{2} \times 7 \frac{2}{3}$

$= \frac{1}{2} \times \frac{23}{3}$

$= \frac{23}{6}$

$= 3 \frac{5}{6}$

The midpoint has coordinates $\left ( 8 \frac{1}{6}, 3 \frac{5}{6} \right )$ .

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Example Question #4 : Graphing Points

In which quadrant or on which axis will you find the point (-3,-4) ?

Possible Answers:

Quadrant I

Quadrant II

Quadrant IV

The -axis

Quadrant III

Correct answer:

Quadrant III

Explanation:

By definition, a point with a negative -coordinate and a negative -coordinate lies in Quadrant III on the coordinate plane.

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Example Question #1 : How To Find A Square On A Coordinate Plane

Vt_custom_xy_xyss2

The above square has an area of 100 square units. What fraction of the area of square is in quadrant II?

Possible Answers:

$\frac{1}{4}$

$\frac{3}{4}$

$\frac{2}{4}$

$\frac{3}{8}$

Correct answer:

$\frac{1}{4}$

Explanation:

To find the fraction of the entire squares area that lays in quadrant II, notice that the square is taking up an equivalent amount in each of the four quadrants. Thus, $\frac{1}{4}$ of the squares area is in quadrant II.

Also note that the area of the square that lays in quadrant II is square units, thus the problem could have alternatively been solved by reducing $\frac{25}{100}=\frac{1}{4}$ .

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Example Question #1 : How To Find A Square On A Coordinate Plane

If a square has an area of square units, what is the perimeter?

Possible Answers:

Correct answer:

Explanation:

In order to solve this problem, apply the formula A=S^2 , in order to conclude that the length of side must equal for the area to equal .

Once you've found the length of side , apply the formula P=4S .

Thus, the solution is $P=4\times7=28$

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Example Question #2 : How To Find A Square On A Coordinate Plane

A square has an area of square units, what is the perimeter?

Possible Answers:

Correct answer:

Explanation:

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Example Question #4 : How To Find A Square On A Coordinate Plane

Vt_custom_xy_xy_ss_square1

Find the perimeter of the square shown above.

Possible Answers:

Correct answer:

Explanation:

To find the perimeter of this square, apply the formula: P=4S , where the length of one side of the square.

Thus, the solution is:

P=4S
$P=4\times6=24$

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SSAT Middle Level Math : Geometry

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

All SSAT Middle Level Math Resources

Example Questions

Example Question #5 : Graphing Points

Example Question #21 : Graphing

Example Question #22 : Graphing

Example Question #1 : How To Find The Points On A Coordinate Plane

Example Question #4 : How To Find The Points On A Coordinate Plane

Example Question #4 : Graphing Points

Example Question #1 : How To Find A Square On A Coordinate Plane

Example Question #1 : How To Find A Square On A Coordinate Plane

Example Question #2 : How To Find A Square On A Coordinate Plane

Example Question #4 : How To Find A Square On A Coordinate Plane

All SSAT Middle Level Math Resources

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