Asked by Miley
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?
What is the x+y?
Answers
Answered by
Reiny
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
(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