# ISEE Middle Level Math : How to find length of a line

## Example Questions

### Example Question #11 : Lines

The coordinates of  on the rectangle are  and . Find the length of the diagonal.

Explanation:

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

### Example Question #12 : Lines

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

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 ,  then the diameter is

### Example Question #13 : Lines

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

Explanation:

The Pythagorean Theorem states that:

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

### Example Question #14 : Lines

What is the perimeter of a right triangle if the hypotenuse is  and the measurement of one of its legs is

Explanation:

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

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

### Example Question #11 : Lines

A line has endpoints  and   What is the distance of the line?

Explanation:

Use the distance formula

### Example Question #16 : Lines

Line  has a length of   It is bisected at point , and the resulting segment is bisected again at point   What is the length of line segment

Explanation:

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

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

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

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

The point  lies on a circle. What is the approximate length of the radius of the circle if the center is

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.

### Example Question #18 : Lines

If the diameter of a circle is , then what is  of the circle's radius?

Explanation:

If the diameter is , then the radius is

Therefore

of  is,

.

### Example Question #19 : Lines

Find the slope of a line that passes through  and .

The slope is undefined.

Explanation:

Use the slope formula to solve:

Given the following points.

The slope can be calculated as follows.

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

### Example Question #20 : Lines

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

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

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

So, let's plug and chug

Simplify