Question

What is R such that PR : RQ = 2/5
Express as a coordinate

Answer 1

From the figure (shown below), the coordinates of P and Q are
P (-2, -2)
Q (4, 8)

Let the point R (x, y) divide the line segment PQ in a 2:5 ratio.
ΔPAR ≈ ΔPBQ because of AAA.
Therefore

`(PA)/(PB) = (2a)/(2a+5a) \\\\ (x+2)/(6)= (2)/(7) \\\\7x+14=12 \\\\ 7x=-2 \\\\ x=- (2)/(7)`

Also,

`(AR)/(BQ)= (2)/(7) \\\\ (y+2)/(10) = (2)/(7) \\\\ 7y+14=20 \\\\ 7y = 6 \\\\ y = (6)/(7)`

Answer:
R has the coordinates (-2/7, 6/7) or (-0.2857, 0.8571)