Question

A particle P(x, y) is moving in the coordinate plane in such a way that dx/dt = -1 m/s and dy/dt = -5 m/s. How fast is the particle's distance from the origin changing as it passes through the point (5, 12)?

Answer 1

if its moving along the plane it should look like this



which to me looks like the equation y=5x+b

Answer 2

r = <5,12> - t<1,5>

x = 5 - t ; x' = -1
y = 12 -5t ; y' = -5

Answer 3

at any rate ... d^2 = x^2 + y^2 gives distance to the origin

2d d' = 2x x' + 2y y'

d' = (xx' +yy')/d

d' = (-5 -5(12))/sqrt(5^2+12^2) looks to be about right