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A garbage truck and a dump truck each drive along a straight road between two points. Using the points on a map that the city created, the garbage truck will start at (–3, 4) and will stop at (5, 12). The dump truck will start at (5, –3) and will stop at (–4, 33).

What are the coordinates of the intersection that both trucks drive through?

Answer :

scme1702
We first find the lines of the motion of each truck, then calculate its intercept.
Garbage truck:
m = (12 - 4) / (5 - 3)
m = 4
4 - y = 4(3 - x)
4x - y = 8

Dump truck:
m = (33 + 3) / (-4 - 5)
m = -4
33 - y = -4(-4 - x)
4x + y = 17

Adding the two equations to solve them, we get:
8x = 25
x = 25 / 8

y = 17 - 4(25/8)
y = 17 - 25/2
y = 9/2

The trucks' point of intersection is (25/8,9/2)

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