How to find length of a line

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SSAT Middle Level Quantitative › How to find length of a line

Questions 1 - 10
1

What is the length of a line with endpoints and .

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!

2

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

Explanation

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

3

A right triangle has one leg with a length of 6 feet and a hypotenuse of 10 feet. What is the length of the other leg?

Explanation

In geometry, a right angle triangle can occur with the ratio of in which 3 and 4 are each leg lengths, and 5 is the hypotenuse.

When you know the length of two sides of a right angle triangle like this, you can calculate the third side using this ratio.

Here, the ratio is:

This is double the ratio. Therefore, we should multiply 4 by 2 in order to solve for the missing leg, which would be a value of 8 feet.

Another way to solve is to use the Pythagorean Theorem: .

We know that one leg is 6 feet and the hypotenuse is 10 feet.

4

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

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:

5

The radius of a circle is 6 inches. What is one-third of the diameter?

Explanation

If the radius is equal to 6 inches, then the diameter will be double that value, or 12 inches. One-third of 12 is 4, which is therefore the correct answer.

6

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

Explanation

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

Plugging in as stated in the question, we find that .

Since the question is asking us for the value of :

.

7

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

Explanation

We can use the distance formula:

8

A right triangle has one leg with length and another leg with length . What is the length of the hypotenuse?

Explanation

Since we are dealing with a right triangle, we can use the Pythagorean Theorem:

,

where and are leg lengths of and , respectively, and is the length of the hypotenuse.

Substituting values into the Theorem:

9

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

R1

Explanation

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

10

Lines

Figure NOT drawn to scale.

Evaluate .

Explanation

By the Segment Addition Postulate,

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