the line segment joining the points A ( 2 , 1 ) B ( 5 , -8 ) is - Maths - Coordinate Geometry

Question

the line segment joining the points A ( 2 , 1 ) B ( 5 , -8 ) is
trisected at the points p and q such that P is nearer to A if P
also lies on the line given by 2 x - y + k =0 , find the value of
k

Lalit Mehra · Accepted Answer

The given point are A(2, 1) and B(5, â€“ 8) Given, P and Q trisects the line segment AB âˆ´ AP = PQ = QB PB = PQ + QB = AP + AP = 2AP AP : PB = AP : 2AP = 1 : 2 âˆ´ P divides the line segment AB in the ration 1 : 2

âˆ´ Coordinates of P $= (\frac{1 \times 5 + 2 \times 2}{1 + 2}, \frac{1 \times (- 8) + 2 \times 1}{1 + 2}) = (\frac{5 + 4}{3}, \frac{- 8 + 2}{3}) = (\frac{9}{3}, \frac{- 6}{3}) = (3, - 2)$ P(3, â€“ 2) lies on 2x â€“ y + k = 0 âˆ´ 2 Ã— 3 â€“ (â€“ 2) + k = 0 â‡’ 6 + 2 + k = 0 â‡’ 8 + k = 0 â‡’ k = â€“ 8 Thus, the value of k is â€“ 8

the line segment joining the points A ( 2 , 1 ) B ( 5 , -8 ) is trisected at the points p and q such that P is nearer to A . if P also lies on the line given by 2 x - y + k =0 , find the value of k.