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)?

y − Q = -5/2(x − P)

y − Q = 2/5(x − P)

y − P = -5/2(x − Q)

y − P = 2/5(x − Q)

A is correct

Step-by-step explanation:

Since the two routes are perpendicular, what this means is that both have the product of their slopes equal to -1

For the first route, we have;

y = (2/5)x -4

Generally the equation of a straight line can be represented by the equation

y = mx + c where m

is the slope. Comparing this with the equation of the old route, the slope here is 2/5

Now the new route is perpendicular, this means that;

m1 * m2 = -1

2/5 * m2 = -1

2m2 = -5

m2 = -5/2

Now we have this line passing through by the point (P, Q)

The equation of this line can be represented by;

y-y1/x-x1 = m

Thus we have;

(y-q)/(x-p) = m

(y-Q)/(x-P) = -5/2

y-Q = -5/2(x-P)

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

step-by-step explanation: