Question

The line segments joining the points (11,-7) and (2,11) is trisected at points P and Q such that P is nearer to A. If point P also lies on the line 8x-5y+k=0, find the value of k and coordinates of Q.

Answer 1

Answer:

A/Q A(11,-7) & B(2,11) . Also P divide AB internally in 1:2 so coordinate of P is..

$( \frac{1 \times 2 + 2 \times 11}{1 + 2} \: \frac{1 \times 11 - 2 \times 7}{1 + 2} ) = (8 \: \: . \: \: - 1)$

P lies on 8x - 5y + k = 0, then 8×8+5×1+k = 0. Hence k = -69 Ans.

now Q divide AB in 2:1 then,

find Q(try your self)