What is the distance of each pair of parallel lines with the given equations y=-x and y=-x-4

Question

step 1- equation of perpendicular line

step2- point of intersection (system of equations)

step 3- distance formula

Answer 1

.Draw a diagram

The distance can be measured along the line y = x (perpendicular to y = -x)

These two lines intersect at (0, 0).

y = x intersects y = -x - 4 at (-2, -2)

 

What is the distance between these two points?

Answer 2

Draw this 'picture' and draw a line perpendicular to those two given parallel lines. Construct a vertical line through one of the intersection points.  That will produce an isosceles right triangle and the hypotenuse will be of length 4. From the Pythagorean theorem you can find that the legs of that triangle are 4 ÷√2 in length, so that's the distance between the given parallel lines.  It can be rationalized to 2√2.

 

Or, follow the steps 1-3 that came with the problem.