Question

Olivia’s house is located at the point (-5, 5) on the coordinate grid. Her best friend Jen’s house is at (2, 3) and the market is at (-5, -5). The movie theater is directly below Jen’s house. The distance from Jen’s house to the movie theater is half the distance from Olivia’s house to the market.

(a) What are the coordinates for the movie theater?
(b) If each unit on the coordinate plane represents ½ mile, how far is Jen’s house from the movie theater?

Answer 1

(a) (2, -2)

(b) 2.5 miles

Explanation:

(a) The distance from Olivia's house (-5, 5) to the market (-5, -5) is the distance from 5 to -5 on the line x=-5. That distance is 5 -(-5) = 10 units.

The distance from Jen's house to the theater is half this, or 5 units. The theater is "directly below" Jen's house, so will have the same x-coordinate, and a y-coordinate that is 5 units less than that of Jen's house. The theater is located at ...

... (2, 3) -(0, 5) = (2, -2) . . . . theater location

(b) The 5 units from Jen's house to the theater represent a distance of ...

... 5 × (1/2 mile) = 5/2 miles = 2.5 miles