IF P (9a-2,b) divides line segment joining A (3a+1,3) and B (8a,5) in the ratio 3:1, find values of a - Maths - Coordinate Geometry

Question

IF P (9a-2,b) divides line segment joining A
(3a+1,3) and B (8a,5) in the ratio 3:1, find values of a and
b?

Santosh Kumar · Accepted Answer

P (9a â€“ 2, b) divides the line segment joining A (3a + 1, 3) and B (8a, 5) in the ratio 3:1 $9 a - 2 = \frac{3 (8 a) + 1 (3 a + 1)}{3 + 1} \Rightarrow 4 (9 a - 2) = 24 a + 3 a + 1 \Rightarrow 36 a - 8 = 27 a + 1 \Rightarrow 36 a - 27 a = 1 + 8 \Rightarrow 9 a = 9 \Rightarrow a = 1 b = \frac{3 (5) + 1 (3)}{4} \Rightarrow 4 b = 15 + 3 \Rightarrow 4 b = 18 \Rightarrow b = \frac{9}{2}$ âˆ´ a = 1 and b = $\frac{9}{2}$

IF P (9a-2,b) divides line segment joining A (3a+1,3) and B (8a,5) in the ratio 3:1, find values of a and b?