Chapter 5.6, Problem 28P

On a map, Sandusky St. passes through coordinates $(2,-1)$ and $(4,8)$.

Pennsylvania Ave. intersects Sandusky St. and passes through coordinates $(1,3)$ and $(6,2)$.

Are these streets perpendicular? Explain.

To determine

To determine if the given lines are perpendicular to each other.

Answer to Problem 28P

They are not perpendicular to each other.

Explanation of Solution

Given information:

Sandusky St. passes through (2, -1) and (4, 8)

Pennsylvania Ave. passes through (1, 3) and (6, 2)

When the line are perpendicular then the product of their slope is equal to -1.

Slope of line with two points is given by,

  $m=\frac{y_2-y_1}{x_2-x_1}$

Hence the slope of Sandusky St. passes through (2, -1) and (4, 8) is $\frac{8-\left(-1\right)}{4-2}=\frac{9}{2}$

Slope of Pennsylvania Ave. passes through (1, 3) and (6, 2) is $\frac{2-3}{6-1}=-\frac{1}{5}$

As product of their slope is not -1.

Hence they are not perpendicular to each other.