Question

A mail truck and a fire truck each drive along a straight road between two points. Using the points on a map that the city created, the mail truck will start at (1, 9) and will stop at (–5, 3). The fire truck will start at (–10, 12) and will stop at (0, 2). What are the coordinates of the intersection that both trucks drive through?

Answer 1

We can use the given points to construct the equations for the mail truck's and fire truck's motion.

Mail truck:
slope = (9 - 3) / (1 + 5)
slope = 1
y - 9 = (x - 1)
y = x + 8

Fire truck
slope = (2 - 12) / (0 + 10)
slope = -1
y - 12 = -1(x + 10)
y = 22 - x

Equating the two:
x + 8 = 22 - x
2x = 14
x = 7

y = x + 8
y = 7 + 8
y = 15

The trucks intercept at the point (7, 15)