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

Central street PQ is perpendicular to AB and intersect the AB street.

Eqn of AB is $y=\frac{7}{3}x-\frac{21.5}{3}$

Slope of PQ = $\frac{-3}{7}$

Eqn of PQ is $y=\frac{-3}{7}x+c$

Now c will have different values depending upon the position of PQ wrt. AB