Answer to Question #217347 in Geometry for ken

Question

Select the correct answer.

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

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

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

$$-1.5x-3.5y=-31.5$$

B. -1.5x − 3.5y = -31.5