Question

Point A is at (2, -8) and point C is at (-4, 7).

Find the coordinates of point B on AC such that the ratio of AB to BC is 2:1.

Answer 1

(-2, 2)

Explanation:

Given:

• Point A is at (2, -8) and point C is at (-4, 7)

Difference of coordinates:

• Δx = 2 - (-4) = 6
• Δy = - 8 - 7 = - 15

The ratio of AB to AC is 2:1. So:

• AB = 2*AC/3 and BC = AC/3

Then coordinates of point B should be 2/3 from the point A:

• x = 2- 6*2/3 = 2 - 4 = -2
• y = - 8 - (-15)*2/3 = -8 + 10 = 2

So point B has coordinates of (-2, 2)