On a map, San St. passes through coordinates (2, –1) and (4, 8). Pen Ave. intersects San St. and passes through coordinates (1, 3) and (6, 2)

Question

 Are these streets perpendicular? Explain.

Answer 1

The first this we need to do is to find the slopes of the lines:

(y₂ - y₁) / (x₂ - x₁)

(8 - (-1)) / (4 - 2)

(8 + 1) / 2

9/2

 

(2 - 3) / (6 - 1)

-1/5

 

Now to compare. When we have perpendicular lines, What we need is the negative reciprocal, so the signs have to be switched, and the numerator and denominators need to be flipped. We can see that the signs have indeed changed, but we don't even have the same numbers in our slope, let alone flipped. Therefore, these streets are not perpendicular.