Question

Points g, k and j are collinear on GJ, and GK:GJ =3/5. G is located at (-4, 5), k is located at (x, y), and J is located at (6, 0). What are the values of x and y?

Answer 1

(x, y) = (2, 2)

Explanation:

The problem statement tells us ...

GK : GJ = 3/5 . . . . the given ratio

5(GK) = 3(GJ) . . . . multiply by 5(GJ)

5(K-G) = 3(J-G) . . . replace segment lengths with endpoint differences

5K -5G = 3J -3G . . . eliminate parentheses

5K = 3J +2G . . . . . add 5G

K = (3J +2G)/5 . . . . divide by 5

K = (3(6, 0) +2(-4, 5))/5 = (18 -8, 0+10)/5 . . . . substitute point coordinates

K = (2, 2)

The values of x and y are both 2.