Question

find the ratio in which the line segment joining the points (-5,8 )and (4,-10) divided by the points (-3, y) also find the value of Y

Answer 1

Let A(-5,8) and B(4,-10) be points of line segment AB divided by C(-3,y)

From the formula - The point which divides a line segment AB in the ratio m:n is given by [(mx₂+nx₁)/(m+n),(my₂+ny₁)/(m+n)] whre A=(x₁,y₁),B=(x₂,y₂)

x-coordinate of C is given by [m*4+n*(-5)]/(m+n) = -3

implies 4m-5n = -3m-3n

implies m:n= 2:7

Using m:n=2:7; y-coordinate of C is given by y=[2*-10+7*8]/(2+7) =  4