ISEE Middle Level Math : Lines

Example Questions

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

Figure NOT drawn to scale.

Evaluate .

Possible Answers:

Correct answer:

Explanation:

By the Segment Addition Postulate,

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

What is the length of a line segment with end points  and ?

Possible Answers:

Correct answer:

Explanation:

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

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

What is the length of a line with endpoints and .

Possible Answers:

Correct answer:

Explanation:

To find the length of this line, you can subtract 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!

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

Find the length of the line segment whose endpoints are and .

Possible Answers:

Correct answer:

Explanation:

We can use the distance formula:

Example Question #71 : Plane Geometry

The point lies on a circle. What is the length of the radius of the circle if the center is located at ?

Possible Answers:

Correct answer:

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:

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

The coordinates of and are and . Find the length of the diagonal of the following rectangle:

Possible Answers:

Correct answer:

Explanation:

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

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:

Correct answer:

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.

Example Question #3 : 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 .

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

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

Possible Answers:

Correct answer:

Explanation:

The Pythagorean Theorem states:

where  represents the hypotenuse and  and  represent the measurements of the legs of the right triangle.

Example Question #5 : 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:

Correct answer:

Explanation:

The Pythagorean Theorem states that

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

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