# SAT Math : How to find the length of a line with distance formula

## Example Questions

### Example Question #11 : Distance Formula

Find the Distance of the line shown below:

Explanation:

The distance formula is . In the graph shown above the coordinates are  and . When you plug the coordinates into the equation you get:

, which then simplifies to

, because  is a prime number there is no need to simplify.

### Example Question #12 : Distance Formula

The endpoints of the diameter of a circle are located at (0,0) and (4, 5). What is the area of the circle?

Explanation:

First, we want to find the value of the diameter of the circle with the given endpoints. We can use the distance formula here:

If the diameter is , then the radius is half of that, or .

We can then plug that radius value into the formula for the area of a circle.

### Example Question #11 : How To Find The Length Of A Line With Distance Formula

What is the distance between the origin and the point ?

Explanation:

The distance between two points  and  is given by the Distance Formula:

Let  and . Substitute these values into the Distance Formula.

To simplify this square root, find a common denominator between the two terms.

Both 4 and  are perfect squares, so we can take their square roots to find

The distance between our two points is .

### Example Question #14 : Distance Formula

One long line segment stretches from  to . Within that line segment is another, shorter segment that spans from  to . What is the distance between the two points on the shorter line segment?

Explanation:

The distance between two points  and  is given by the following formula:

Let  and let . When we plug these two coordinates into the equation we get:

### Example Question #15 : Distance Formula

Find the distance from the center of the given circle to the point .

Explanation:

Remember that the general equation of a circle with center  and radius  is

With this in mind, the center of our circle is . To find the distance from this point to , we can use the distance formula.

### Example Question #16 : Distance Formula

The following points represent the vertices of a box. Find the length of the box's diagonal.

Explanation:

To solve this problem let's choose two vertices that lie diagonally from one another. Let's choose  and

We can plug these two points into the Distance Formula, and that will give us the length of the box's diagonal.

### Example Question #17 : Distance Formula

What is the length of the line between the points  and ?

Explanation:

Step 1: We need to recall the distance formula, which helps us calculate the length of a line between the two points.

The formula is: , where distance and  are my two points.

Step 2: We need to identify .

Step 3: Substitute the values in step 2 into the formula:

Step 4: Start evaluating the parentheses:

Step 5: Evaluate the exponents inside the square root

Step 7: We need to evaluate  in a calculator

### Example Question #18 : Distance Formula

Give the length, in terms of , of a segment on the coordinate plane whose endpoints are   and .

Explanation:

The length of a segment with endpoints  and  can be calculated using the distance formula:

Setting  and  and substituting:

The binomials can be rewritten using the perfect square trinomial pattern:

Simplify and collect like terms:

### Example Question #19 : Distance Formula

In terms of , give the length of a segment on the coordinate plane with endpoints  and .

Explanation:

The length of a segment with endpoints  and  can be calculated using the distance formula:

Setting  and , and substituting:

The binomials can be rewritten using the perfect square trinomial pattern:

Simplify and collect like terms:

### Example Question #20 : Distance Formula

Give the length, in terms of , of a line segment on the coordinate plane whose endpoints are  and .