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ISEE Middle Level Math : Plane Geometry

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Example Question #81 : Geometry

If a circle has a radius of 8cm , what would be the length of the longest line drawn within that circle?

Possible Answers:

16cm

15cm

10cm

4cm

Correct answer:

16cm

Explanation:

The diameter of the circle would be the longest line that can be drawn within that circle.

Because radius is half of the diameter, the diameter is calculated by multiplying the radius of the circle by two.

If the radius is 8cm , then the diameter is $8m \times 2 = 16m$

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Example Question #82 : Geometry

A ladder is leaning on a wall. It is 16ft ft long. The bottom of the ladder is 10ft from the base. How far up the wall is the top of the ladder?

Possible Answers:

$\approx 12.5ft$

$\approx13.5ft$

$\approx 14ft$

$\approx11.5ft$

Correct answer:

$\approx 12.5ft$

Explanation:

The Pythagorean Theorem states that:

$a^{2} +b^{2} = c^{2}$

With and representing the measurement of the legs and representing the hypotenuse.

$10^{2} +b^{2} = 16^{2}$

$100 + b^{2} = 256$

$(100-100) + b^{2} = 256-100$

$b^{2} = 156$

$\sqrt{b^{2}} = \sqrt{156}$

$b\approx 12.5ft$

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Example Question #83 : Geometry

What is the perimeter of a right triangle if the hypotenuse is 15cm and the measurement of one of its legs is 9cm?

Possible Answers:

12cm

36cm

39cm

33cm

Correct answer:

36cm

Explanation:

First, use the Pythagorean Theorem to get the measurement of the other leg.

$a^{2} +b^{2} =c^{2}$

$9^{2} + b^{2} =15^{2}$

$81 + b^{2} = 225$

$(81-81) + b^{2} = 225-81$

$b^{2} = 144$

b = 12cm

To get the perimeter of the triangle, add the measurements of each of the three sides.

9 + 15 + 12 = 36cm

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Example Question #84 : Geometry

A line has endpoints (7,9) and (1,1). What is the distance of the line?

Possible Answers:

d = 14

d = 10

d = 12

d = 8

Correct answer:

d = 10

Explanation:

Use the distance formula

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

$d=\sqrt{(7-1)^{2} + (9-1)^{2}}$

$d=\sqrt{36+64}$

$d = \sqrt{100}$

d = 10

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Example Question #11 : Lines

Line has a length of 80cm. It is bisected at point , and the resulting segment is bisected again at point What is the length of line segment AD?

Possible Answers:

20cm

30cm

50cm

40cm

Correct answer:

20cm

Explanation:

First, write each portion of the statement in mathematical terms.

$AC =\frac{1}{2} AB$

Since AB=80 we will substitute that into the equation.

$AC =\frac{1}{2} (80)$

AC = 40

Now that we know AC we can calculate AD as follows.

$AD = \frac{1}{2} AC$

$AD = \frac{1}{2}(40)$

AD = 20cm

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Example Question #86 : Geometry

The point (2,-2) lies on a circle. What is the approximate length of the radius of the circle if the center is (3,-5) ?

Possible Answers:

$d\approx5$

$d\approx 7$

$d=\sqrt{10}$

$d=\sqrt{5}$

Correct answer:

$d=\sqrt{10}$

Explanation:

Because the radius is the distance from center to any point on a circle, the distance formula is used to find the measurement of the radius.

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

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

$1^{2} = 1\times1 = 1$

$-3^{2} = -3\times -3 = 9$

$d = \sqrt{1+9}$

$d =\sqrt{10}$

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Example Question #87 : Geometry

If the diameter of a circle is 12cm , then what is $\frac{1}{3}$ of the circle's radius?

Possible Answers:

2cm

4cm

10cm

8cm

Correct answer:

2cm

Explanation:

Radius is $\frac{1}{2}$ of the diameter.

If the diameter is 12cm , then the radius is 6m.

$\frac{1}{2}\cdot \frac{12}{1}=\frac{12}{2}=\frac{2\cdot6}{2}=6$

Therefore

$\frac{1}{3}$ of 6cm is,

$\frac{1}{3}\cdot \frac{6}{1}=\frac{6}{3}=\frac{3\cdot 2}{3}=2cm$ .

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Example Question #88 : Geometry

Find the slope of a line that passes through A (-5,-1) and B (3,-1) .

Possible Answers:

m = -1

The slope is undefined.

m = 8

m = 0

Correct answer:

m = 0

Explanation:

Use the slope formula to solve:

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

Given the following points.

A (-5,-1)=(x_1,y_1)

B (3,-1)=(x_2,y_2)

The slope can be calculated as follows.

$m = \frac{-1 - (-1)}{3- (-5)}$

$m = \frac{0}{8}$

m = 0

Because the coordinates were the same for points A and B, this would form a horizontal line. The slope of any horizontal line is

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Example Question #89 : Geometry

Find the length of a line from the point to the point .

Possible Answers:

30.4

Correct answer:

30.4

Explanation:

Find the length of a line from the point to the point .

To find this distance, we need to use distance formula (which is really similar to Pythagorean Theorem)

Distance formula is as follows

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

Where our x's and y's come from our ordered pairs.

So, let's plug and chug

$d=\sqrt{(9--12)^2+(14-36)^2}$

Simplify

$d=\sqrt{(21)^2+(-22)^2}$

$d=\sqrt{441+484}=\sqrt{925}\approx30.4$

So our answer is 30.4

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Example Question #90 : Geometry

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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ISEE Middle Level Math : Plane Geometry

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #81 : Geometry

Example Question #82 : Geometry

Example Question #83 : Geometry

Example Question #84 : Geometry

Example Question #11 : Lines

Example Question #86 : Geometry

Example Question #87 : Geometry

Example Question #88 : Geometry

Example Question #89 : Geometry

Example Question #90 : Geometry

All ISEE Middle Level Math Resources

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