HELP FAST 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?
A. -3x + 4y = 3
B. -1.5x − 3.5y = -31.5
C. 2x + y = 20
D. -2.25x + y = -9.75

Step-by-step explanation:

Given

AB:

Required

Determine the equation of PQ

First, we calculate the slope of AB:

Make 3y the subject

Make y the subject

An equation has the general form:

Where m = slope

So:

-- Slope of AB

From the attached diagram, we can see that PQ is perpendicular to AB.

This means that, the relationship between their slope is:

Substitute 7/3 for m1

The equation of PQ is then calculated as:

Where

and

So, we have:

Multiply both sides by 7

Open bracket

Collect Like Terms

Divide through by -1/2

The equation of PQ is:

(-1,-0.5)

step-by-step explanation:

step-by-step explanation: