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 = two fifthsx − 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 = negative five halves(x − P) y − Q = two fifths(x − P) y − P = negative five halvesx − Q) y − P = two fifths(x − Q)

Answer 1

Answer:

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

Step-by-step explanation:

on flvs geometry module 4 test, this is correct!

Answer 2

The equation of the new route if it is to be perpendicular to the old route and will go through point (P, Q) is $y - Q = -\frac{5}{2}(x - P)$

Since the equation of the path of the old route can be described as y = two fifthsx − 4, it is $y = \frac{2}{5}(x - 4)$

Now the gradient of this old route is m = 2/5.

Since the new route is perpendicular to the old route, if we let its gradient be  m', then mm' = -1 (since the routes are perpendicular).

So, m' = -1/m

m' = -1/2/5

m' = -5/2

So, the gradient of the new route is m' = -5/2.

Since the new route passes through the point (P, Q), the equation of the new route passing through this point is given by

(y - Q)/(x - P) = m'.

$\frac{y - Q}{x - P} = m'$

This is the equation of the new route given in gradient form where m' is the gradient of the new route.

Since m' = -5/2,

$\frac{y - Q}{x - P} = m'$

$\frac{y - Q}{x - P} = -\frac{5}{2}$

$y - Q = -\frac{5}{2}(x - P)$

So, the equation of the new route if it is to be perpendicular to the old route and will go through point (P, Q) is $y - Q = -\frac{5}{2}(x - P)$

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