Question

The point B lies on the segment AC.

Find the coordinates of B so that the ratio of AB to B C is 5 to 4.

A(-6,5)

B(?,?)

C(21,-13)

Answer 1

(9, -5)

Explanation:

The vector AC has coordinates (27, -18), because:

21 - (-6) = 27

-13 - 5 = -18

If the ratio of AB to BC is 5 to 4, it means that

AB = [5/(5+4)]AC = (5/9)AC

Therefore, we have

AB = (5/9)AC = (5/9) (27, -18) = (15, -10)

Which means that:

xB - xA = 15 <=> xB - (-6) = 15 <=> xB + 6 = 15 <=> xB = 9

yB - yA = -10 <=> yB - 5 = -10 <=> yB = -10 + 5 <=> yB = -5

So B has coordinates (9, -5).