What is the approximate distance between points a and b?

For this problem we will use the Pythagorean Theorem. 

a^2 + b^2 = c^2

Since we are trying to find C, or the hypotenuse.  The hypotenuse is the longest side of the triangle.

What triangle?

Starting at Point A draw a line all the way down to -4.

At Point B draw a line all the way to the right to 4.

Here you have your right triangle. 

Side A, the side opposite from Angle A is 6 units.

Side B, the side opposite from Angle B is 7 units.

Now we will plug this into the Pythagorean Theorem.

6^2 + 7^2= c^2

36+49= 85 

The square root of 85 is approximately 9.2 units.