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 $-7x + 3y = -21.5$

this could be written as $y=\dfrac{7x}{3}-\dfrac{21.5}{3}$

slope of this line is 7/3

central street PQ will be perpendicular to the lane passing through A and B

slope of central street PQ = $\dfrac{-1}{slope \ of\ lane \ joining \ A\ and \ B}=\dfrac{-1}{7/3}=\dfrac{-3}{7}$

Equation of the central street PQ .

$y=mx+c$

$y=-3x/7 \ +c$