Answer to Question #217134 in Geometry for sleepy

Question

A software designer is mapping the streets for a new racing game. All of the streets are depicted as either perpendicular or parallel lines. The equation of the lane passing through A and B is -7x + 3y = -21.5. What is the equation of the central street PQ?

Answer 1

The equation of the lane passing through $A$ and $B,$ is

$$-7x+3y=-21.5$$

Solve for $y$

$$y=\dfrac{7}{3}x-\dfrac{43}{6}$$

Hence

$$slope_1=\dfrac{7}{3}$$

Since the central street $PQ$ is perpendicular to the lane passing through $A$ and $B,$ then

$$slope_2=\dfrac{-1}{slope_1}=-\dfrac{3}{7}$$

Point $P(7, 6)$

$$6=-\dfrac{3}{7}(7)+b=>b=9$$

The equation of the central street $PQ$ is

$$y=-\dfrac{3}{7}x+9$$