# How do you find the possible values for a if the points (a,6), (-6,2) has a distance of #4sqrt10#?

##### 2 Answers

See a solution process below:

#### Explanation:

The formula for calculating the distance between two points is:

Substituting the values for the distance and from the points in the problem gives:

We can now solve for

First, square both sides of the equation to eliminate the radicals while keeping the equation balanced:

We can factor this as:

#0 = (a + 18)(a - 6)

Now, equate each term on the right side of the equation to

Solution 1)

Solution 3)

The solution is, a could be

or

#### Explanation:

**Distance between two points**,

=

*In this case*

**Carry out factorisation**

**Divide RHS #(0)# with #(a+18)# and #(a-6)#**

*You will have*

*which give you*

*respectively*