Question

If the point (x, y) is one-third of the way from (-2, 6) to (6,-8), then what is x + y?

What is the x+y?

Answer 1

for the x:
(x+2)/(6+2) = 1/3
3x + 6 = 8
3x = 2
x = 2/3

for the y:
(y-6)/(-8-6) = 1/3
3y - 18 = -14
3y = 4
y = 4/3

(x,y) = (2/3,4/3)

check: distance form (-2,6) to (2/3,4/3)
= √( (-2-2/3)^2 + (6-4/3)^2
= √( 64/9 + 196/3)
=√(260/9)
= (1/3)√260

distance from (-2,6) to 6,-8)
= √( 64 + 196)
= √260

so the distance checks out

x+y = 2/3 + 4/3 = 6/3 = 2