# Thread: Lines in a Plane 15

1. ## Lines in a Plane 15

You are driving from point A(24,96) on a map grid towards point B with a velocity defined by d=(85,-65) km/h

a) state the parametric eqtns of the highway line.
b) how long have you been traveling when you reach a point P 102 km east of where you started at point A?
c) what are the coordinates of your position P at that time?

so this is my work below, I need help with parts b and c.

a) x=24+85t
y=96-65t

b) d=AB
(85,-65)=(x-24)(y-96)
x-24=85
x=109
y-96=-65
y=31
|AB|=sqrt (11450)

(11450)^ (0.5) +102 = 209

d/s=t
209/(-65/85)=273 h

The answer in the back is 55 min

c) P(194,-34)

How do I get their answers and what did I do wrong?

2. $\displaystyle x=24+85t$

Since we are due east, we can use x=102.

$\displaystyle 102=24+85t$

$\displaystyle t=.917647$

This is hours. Multiply by 60 and get 55.05 minutes.

part c, y=96-65(.917647)=36.35

The coordinates are (102, 36.35)

I think you just had a small mental block. You have the right equations.