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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 #61 : Geometry

Lines

Figure NOT drawn to scale.

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

Evaluate .

Possible Answers:

8.6

9.6

7.2

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 #4 : Lines

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 #72 : Plane Geometry

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 #3 : Lines

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:

4.4

4.12

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 #1 : How To Find Length Of A Line

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

Possible Answers:

3.6

4.6

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 #1 : 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:

$14\ \textup{inches}$

$26\ \textup{inches}$

$20\ \textup{inches}$

$24\ \textup{inches}$

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 #4 : How To Find Length Of A Line

If you stand on a giant number line at point , what is your distance from point ?

Possible Answers:

Correct answer:

Explanation:

The distance on a number line is the number of whole number places between two numbers. When you are going from a negative value to a positive one or vice versa, you must find the distance from that both points are then add them together. is spaces away from and is spaces away. To find the distance you then add your two values of and to get .

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Example Question #1 : Lines

One of the legs on a right triangle has a measurement of 30cm and the other leg has a measurement of 40cm. What is the length of the hypotenuse?

Possible Answers:

1200cm

70cm

50cm

10cm

Correct answer:

50cm

Explanation:

The Pythagorean Theorem states:

$a^{2 } +b^{2} =c ^{2}$ where represents the hypotenuse and and represent the measurements of the legs of the right triangle.

$30^{2} = 30 \times30 = 900$

$40^{2} = 40 \times 40 = 1600$

900 + 1600 = 2500

$\sqrt{c^{2}} = \sqrt{2500}$

c = 500 cm

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Example Question #6 : How To Find Length Of A Line

A right triangle has one leg with a length of and a hypotenuse of . What is the approximate measurement of the missing length?

Possible Answers:

$b\approx 11cm$

$b\approx 7.4cm$

$b \approx 9.5cm$

$b\approx 8.3cm$

Correct answer:

$b\approx 7.4cm$

Explanation:

The Pythagorean Theorem states that

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

Where and are the measurements of each leg and is the hypotenuse.

$3^{2} = 3 \times3 =9$

$8^{2} = 8\times 8 = 64.$

$9 + b^{2} = 64$

$(9-9) + b^{2} = 64-9$

$b^{2} = 55$

$\sqrt{b^{2}} = \sqrt{55}$

$b\approx 7.4cm$

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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 #61 : Geometry

Example Question #4 : Lines

Example Question #72 : Plane Geometry

Example Question #3 : Lines

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

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

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

Example Question #4 : How To Find Length Of A Line

Example Question #1 : Lines

Example Question #6 : How To Find Length Of A Line

All ISEE Middle Level Math Resources

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