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ISEE Middle Level Math : Lines

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

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Example Questions

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

Rec

The coordinates of on the rectangle are D (5,2) and B (7,-3) . Find the length of the diagonal.

Possible Answers:

$d \approx 4.4$

$d\approx 6.4$

$d \approx 5.4$

$d\approx 7.4$

Correct answer:

$d \approx 5.4$

Explanation:

A rectangle has two diagonals with the same length. Therefore, use the distance formula to calculate the distance.

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

$(7-5)^{2} = 2^{2} = 4$

$(-3-2)^{2} = -5^{2} = 25$

$\sqrt{4+25}$

$\sqrt{29} \approx 5.4$

$d \approx 5.4$

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Example Question #11 : Lines

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

Possible Answers:

16cm

4cm

10cm

15cm

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 #12 : How To Find Length Of A Line

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:

$\approx 12.5ft$

$\approx11.5ft$

$\approx13.5ft$

$\approx 14ft$

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 #13 : How To Find Length Of A Line

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:

36cm

39cm

12cm

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 #14 : How To Find Length Of A Line

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

Possible Answers:

d = 12

d = 14

d = 10

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 #15 : How To Find Length Of A Line

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:

30cm

50cm

40cm

20cm

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 #13 : How To Find Length Of A Line

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:

$d=\sqrt{10}$

$d\approx 7$

$d=\sqrt{5}$

$d\approx5$

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 #14 : How To Find Length Of A Line

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

Possible Answers:

10cm

4cm

8cm

2cm

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 #12 : Lines

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

Possible Answers:

m = 0

m = 8

The slope is undefined.

m = -1

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 #16 : How To Find Length Of A Line

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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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Lines

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

All ISEE Middle Level Math Resources

Example Questions

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

Example Question #11 : Lines

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

Example Question #13 : How To Find Length Of A Line

Example Question #14 : How To Find Length Of A Line

Example Question #15 : How To Find Length Of A Line

Example Question #13 : How To Find Length Of A Line

Example Question #14 : How To Find Length Of A Line

Example Question #12 : Lines

Example Question #16 : How To Find Length Of A Line

All ISEE Middle Level Math Resources

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