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SSAT Middle Level Math : Geometry

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Example Questions

Example Question #2 : How To Find Length Of A Line

Lines

Figure NOT drawn to scale.

AE = 40, AB = x, BC = x + 3, CD = 2x, DE = x-6

Evaluate .

Possible Answers:

7.2

8.6

9.6

6.2

Correct answer:

8.6

Explanation:

By the Segment Addition Postulate,

AB + BC + CD + DE = AE

x +( x + 3) +( 2x) +( x-6) = 40

5x-3 = 40

5x-3 +3 = 40 + 3

5x = 43

$5x \div 5 = 43 \div 5$

x = 8.6

AB = x = 8.6

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Example Question #3 : How To Find Length Of A Line

What is the length of a line segment with end points (3,5) and (6,1) ?

Possible Answers:

Correct answer:

Explanation:

The length of a line segment can be determined using the distance formula:

$D=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2}$

$D=\sqrt{(3-6)^2+(5-1)^2}$

$D=\sqrt{-3^2+4^2}$

$D=\sqrt{9+16}=\sqrt{25}=5$

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Example Question #1 : How To Find Length Of A Line

What is the length of a line with endpoints (1,1) and (10,1) .

Possible Answers:

Correct answer:

Explanation:

To find the length of this line, you can subtract 10-1 to get . Since the y-coordinates are the same, you don't have to take any vertical direction into account. Therefore, you only look at the x-coordinates!

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Example Question #182 : Plane Geometry

Find the length of the line segment whose endpoints are (-3,5) and (5,4) .

Possible Answers:

8.06

Correct answer:

8.06

Explanation:

We can use the distance formula:

$D=\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2}$

$=\sqrt{(-3-5)^2+(5-4)^2}$

$=\sqrt{64+1}$

$=\sqrt{65}\approx 8.06$

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Example Question #2 : How To Find Length Of A Line

The point (4,4) lies on a circle. What is the length of the radius of the circle if the center is located at (3,8) ?

Possible Answers:

4.12

4.4

3.12

Correct answer:

4.12

Explanation:

The radius is the distance from the center of the circle to anypoint on the circle. So we can use the distance formula in order to find the radius of the circle:

$D=\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2}$

$=\sqrt{(4-3)^2+(4-8)^2}$

$=\sqrt{1+16}$

$=\sqrt{17}\approx 4.12$

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Example Question #3 : Lines

The coordinates of and are A(4,1) and D(7,-1) . Find the length of the diagonal of the following rectangle:

Possible Answers:

4.6

3.6

Correct answer:

3.6

Explanation:

A rectangle has two diagonals with the same length. So we should find the length of . We can use the distance formula:

$D=\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2}$

$=\sqrt{(4-7)^2+(1+1)^2}$

$=\sqrt{9+4}$

$=\sqrt{13}\approx 3.6$

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Example Question #11 : How To Find Length Of A Line

If a circle has a radius of 12 inches, the biggest line that would be drawn within the circle is:

Possible Answers:

$14\ \textup{inches}$

$26\ \textup{inches}$

$24\ \textup{inches}$

$20\ \textup{inches}$

Correct answer:

$24\ \textup{inches}$

Explanation:

The largest line that can be drawn within a circle is the diamater. The diameter is equal to twice the radius. Given that the radius is equal to 12 inches, the largest line that could be drawn (the diameter) would be equal to 24 inches.

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Example Question #12 : How To Find Length Of A Line

The diameter of a circle is centimeters. What is one-fourth of the circle's radius?

Possible Answers:

$6\:cm$

$8\:cm$

$4\:cm$

$12\:cm$

Correct answer:

Explanation:

By definition, the radius (r) and diameter (d) of a circle are related by the following equation:

d=2r

Plugging in d=16 as stated in the question, we find that r=8 .

Since the question is asking us for the value of $\frac{1}{4}r$ :

$\frac{1}{4}r=\frac{1}{4}(8)=\frac{8}{4}=2\:cm$ .

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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 #2 : How To Find Length Of A Line

Example Question #3 : How To Find Length Of A Line

Example Question #1 : How To Find Length Of A Line

Example Question #182 : Plane Geometry

Example Question #2 : How To Find Length Of A Line

Example Question #3 : Lines

Example Question #11 : How To Find Length Of A Line

Example Question #12 : How To Find Length Of A Line

All SSAT Middle Level Math Resources

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