High School Math : How to find the length of a line with distance formula

Example Questions

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Example Question #17 : Coordinate Geometry

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

Explanation:

The formula for the length of line is the distance formula, which is very similar to the Pythagorean theorem.

Plug in the given values and solve for the length.

Example Question #18 : Coordinate Geometry

What would be the length of a line with endpoints at  and ?

Explanation:

The formula for the length of line is the distance formula, which is very similar to the Pythagorean theorem.

Plug in the given values and solve for the length.

Example Question #19 : Coordinate Geometry

What line goes through the points and ?

Explanation:

Find the slope between the two points:

Next, use the slope-intercept form of the equation:

or where

So the equation becomes or in standard form .

Example Question #20 : Coordinate Geometry

What is the length of a line with endpoints at  and ?

Explanation:

The formula for the length of a line is very similiar to the pythagorean theorem:

Plug in our given numbers to solve:

Example Question #1 : How To Find The Length Of A Line With Distance Formula

What is the length of a line with endpoints at  and ?

Explanation:

The formula for the length of a line is very similiar to the pythagorean theorem:

Plug in our given numbers to solve:

Example Question #2 : How To Find The Length Of A Line With Distance Formula

Find the distance between points  and .

Explanation:

Use the distance formula:

Substitute the given points into the formula:

Example Question #3 : How To Find The Length Of A Line With Distance Formula

What is the length of a line with endpoints of and ?

Explanation:

The distance formula is just a reworking of the Pythagorean theorem:

Expand that.

Plug in our given values.

Example Question #4 : How To Find The Length Of A Line With Distance Formula

What is the distance between and ?

Explanation:

Let and .

The distance formula is given by .

Substitute in the given points:

Example Question #5 : How To Find The Length Of A Line With Distance Formula

A line segment has endpoints at  and . What is the distance of this segment?

Explanation:

To find the distance, we use the distance formula: .

Expand that:

Plug in our given values.

Example Question #6 : How To Find The Length Of A Line With Distance Formula

If a line has a length of , and the endpoints are  and , what is the value of ?

Explanation:

The formula for the length of a line, l, is the distance formula, which is very similar to the Pythagorean Theorem.

Note that the problem has already given us a value for the length of the line. That means . Plug in all of the given values and solve for the missing term.

Subtract  from both sides.

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