Question

A city planner is rerouting tratfic in order to work on a stretch of road. The equation of the path of the oild route can be described as y= 2/5 x-4 I. What should the equation of the new route be if it is to be parpendicular to the old route and will go through point (P. Qy?

a. y-0=- 5/2 (x-P)
b. y-Q= 2/5 (x-P)
c. y-P=- 5/2 x-Q
d. y-P= 2/5 (x-Q)

Answer 1

The correct equation for the new route that is perpendicular to the old route and passes through (P, Q) is y - Q = -5/2 (x - P).

Step-by-step explanation:

The equation of the new route should be perpendicular to the old route. The slope of the old route is 2/5, so the slope of the perpendicular line must be the negative reciprocal, which is -5/2.

To ensure that the new route passes through point (P, Q), we use the point-slope form of the equation of a line. This gives us the correct choice as a. y - Q = -5/2 (x - P), because it has the correct slope and passes through the given point (P, Q).