Answer to Question #142992 in Analytic Geometry for justus

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

y=mx+c

-7x+3y=31.5

3y= -31.5+7x

y= 7/3x -43/6

Here m= 7/3

We know that the line passing through AB is perpendicular to the line passing through PQ from the full question

m₁ = -1/m₂

m₂ = slope of PQ = -1/(7/3) = -3/7

y-y₁ = m(x-x₁)

y-6 = -3/7(x-7)

7y-42= -3x + 21

7y+3x = 21+42

7y +3x = 63