A city planner is rerouting traffic in order to work on a stretch of road. The equation of the path of the old route can be described as y = 2/5x − 4.

What should the equation of the new route be if it is to be perpendicular to the old route and will go through point (P, Q)?

A. y − Q = -5/2(x − P)
B. y − Q = 2/5(x − P)
C. y − P = -5/2x − Q)
D. y − P = 2/5(x − Q)

Question

A city planner is rerouting traffic in order to work on a stretch of road. The equation of the path of the old route can be described as y = 2/5x − 4.

What should the equation of the new route be if it is to be perpendicular to the old route and will go through point (P, Q)?

A. y − Q = -5/2(x − P)
B. y − Q = 2/5(x − P)
C. y − P = -5/2x − Q)
D. y − P = 2/5(x − Q)

Vocaloid · Answer

point slope form:

y - y1 = m(x-x1)

starting with the original line: y = (2/5)x - 4
if the new route is perpendicular, the new slope m must be the negative reciprocal of the old slope 2/5. calculate the new m value.

after that, since it passes through (P,Q), you can let these be your (x1,y1) values in the point slope formula