Question

Point A is located at (2, 8) and point B is located at (8, 5). What point partitions the directed line segment ​ AB⎯⎯⎯⎯⎯ ​ into a 1:3 ratio? (3 1/2, 7 1/4) (3 1/3, 4 1/3) (6 1/2, 5 1/4) (2 1/2, 3 1/4)

Answer 1

3 & 1/2 AND 7 & 1/4

Explanation:

Answer 2

(3 1/2, 7 1/4)

Explanation:

When the segments have the ratio 1:3, the shorter segment is 1/(1+3) = 1/4 of the total length.

The point P that divides the length that way will be ...

... P = A + (1/4)(B - A)

... = A - 1/4A + 1/4B

... = (3A +B)/4

... = (3(2, 8) +(8, 5))/4 = (14/4, 29/4)

... P = (3 1/2, 7 1/4)