Question

A coordinate plane is labeled Street on the x-axis and Avenue on the y-axis. Ping is at point (3, 6) and Ari is at point (21, 18). A line is drawn from Ping to Ari.
Ping lives at the corner of 3rd Street and 6th Avenue. Ari lives at the corner of 21st Street and 18th Avenue. There is a gym Two-thirds the distance from Ping's home to Ari's home.

x = (StartFraction m Over m + n EndFraction) (x 2 minus x 1) + x 1

y = (StartFraction m Over m + n EndFraction) (y 2 minus y 1) + y 1

Where is the gym?

9th Street and 10th Avenue
12th Street and 12th Avenue
14th Street and 12th Avenue
15th Street and 14th Avenue

Answer 1

Compute 2/3 of the vector from Ping to Ari and add to Ping:

x = 3 + (2/3)(21 − 3) = 3 + (2/3)(18) = 3 + 12 = 15
y = 6 + (2/3)(18 − 6) = 6 + (2/3)(12) = 6 + 8 = 14

So the gym is at 15th Street and 14th Avenue.