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

## Example Questions

### Example Question #391 : Geometry

What is the distance between and ?

Explanation:

The distance formula is .

Let  and :

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

What is the distance between and ?

Explanation:

The distance formula is given by .

Let and :

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

What is the distance between and ?

Explanation:

The distance formula is given by .

Let  and :

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

What is the distance between the points and ?

Explanation:

The distance formula is .

Let and .

Plug these two points into the distance formula:

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

If a line with a length of 5 starts at the point , which of the following is NOT a possible end point?

Explanation:

Let , and let be the end point we are looking for.

Recall the distance formula:

Squaring the distance formula gives .

Plug this squared distance formula and solve for :

Substitute each response into this equation to see which one is false.  The only response that doesn't work is .

### Example Question #401 : Geometry

What is the distance between and ?

Explanation:

The distance formula is .

Let and .

Plug these points into the distance formula:

### Example Question #7 : How To Find Length Of A Line

If a line that is 13 inches in length starts at the point , which of the following is NOT a possible end point?

Explanation:

The distance formula is given by .

Square both sides:

Now, let , and let be the end point we are looking for.

Plug into the squared distance formula and solve for :

Alternatively, you can plug in the answer choices and see which point makes the above equation untrue.  The point matches this description and is therefore the correct answer.

### Example Question #8 : How To Find Length Of A Line

How long is a line segment on the number line if it goes from  to ?

Explanation:

To find the length of a line on the number line when one point is negative and the other is positive, you must the the distances of both from zero.   is  spaces from zero where is the other point is just .  So the distance is .

### Example Question #9 : How To Find Length Of A Line

What is the distance between  and