Expert: Sherman D. - 6/14/2008

Question
The endpoint of segment AB are :
point A (1, -5)
point B (9, 11)

find the coordinates of the point 7/8 of the way from A to B.


can u plz help me.

Answer
(1,-5) and (9,11)

M = (9 + 1)/2, (11 - 5)/2
M = 10/2, 6/2
M = 5,3

this is for 4/8 or 1/2 the distance

(5,3) and (9,11)
M = (9 + 5)/2, (11 + 3)/2
M = 14/2, 14/2
M = 7,7

(7,7) and (9,11)
M = (9 + 7)/2, (11 + 7)/2
M = 16/2, 18/2
M = 8,9

ANS : (8,9)

Proof

(1,-5) and (9,11)
D = sqrt((9 - 1)^2 + (11 - (-5))^2)
D = sqrt(8^2 + 16^2)
D = sqrt(64 + 256)
D = sqrt(320)
D = sqrt(64 * 5)
D = 8sqrt(5)

You need the distance to be (7/8) the distance from A to B, this is the same as saying (1/8) the distance from B to A.

(1/8)(8sqrt(5)) = sqrt(5)

(8,9) and (9,11)
D = sqrt((9 - 8)^2 + (11 - 9)^2)
D = sqrt(1^2 + 2^2)
D = sqrt(1 + 4)
D = sqrt(5)

This was easy only because

(1/2) the distance from A to B, + half the distance from M1 to B, + half the distance from M2 to B = (7/8)

in otherwords

(1/2) + (1/4) + (1/8) = (7/8)