Question

Find the point, M, that divides segment AB into a ratio of 5:2 if A is at (1, 2) and B is at (8, 16).

A) (6, 12)
B) (-6, 12)
C) (6, -12)
D) (-6, -12)
*Please explain how you got your answer. It would really help me:)*

Answer 1

A

Explanation:

Answer 2

The x-coordinate of the point will be 1 + (5/7)*(8-1) = 6.
This is because you start out with the original x-coordinate at point A, which is 1. Then you add the result you get from multiplying the distance between x-coordinates (8-1) by 5/7, which is from the ratio 5:2. There are 5 parts out of the 7 parts (7 parts because 5+2).

The y-coordinate of the point will be 2 + (5/7)*(16-2) = 12
This is because you start out with the y-coordinate of point A, which is 2. Then you add the result you get by multipling the distance between y-coordinates by 5/7.