# What is the distance between parallel lines whose equations are y=-x+2 and y=-x+8?

##### 1 Answer

Distance:

#### Explanation:

Giving us the points

The vertical distance between the two lines is the vertical distance between

The horizontal distance between the two lines is the horizontal distance between

Consider the triangle formed by these

The length of the hypotenuse (based on the Pythagorean Theorem) is

The area of the triangle using the horizontal vertical sides is

But we can also get this area using the perpendicular distance from the hypotenuse (let's call this distance

Note that

#"Area"_triangle = 1/2 * 6sqrt(2) * d " sq.units

Combining our two equations for the area gives us