Question

A (30, 20) and B ( 6, -4) are two fixed points. Find the coordinates of a point Pin AB such that 2PB = AP. Also, find the coordinates of some other point Qin AB such that AB = 6 AQ. 

Answer 1

2 PB = AP 

⇒ `"AP"/"PB" = 2/1`

⇒ Coordinates of P are 

P (x , y) = P `((2 xx 6 + 1 xx 30)/(2 + 1), (2 xx -4 + 1 xx 20)/(2 + 1))`

= P (14 , 4)

AB : AQ = 6 : 1

AQ : QB = 1 : 5 

Coordinates of Q are 

Q (a , b) = Q `((1 xx 6 + 5 xx 30)/(1 + 5) , (1 xx -4 + 5 xx 20)/(2 + 1))` = Q (26 , 16)