Find the coordinates of the point that divides AB in the ratio given (a)A(-1,4),B(3,1) 1:2 internally (b) A(3,5),B(-2,3) 3:2 externally?

1 Answer
Sep 19, 2015

(a)(x,y)=(1/3,3)

(b)(x,y)=(-12,-1)

Explanation:

(a) If (x,y) divides the line joining the point

A(x_1,y_1)=(-1,4) and B(x_2,y_2)=(3,1)

INTERNALLY in the ratio lambda:mu = 1:2, then;

(x,y)=((lambdax_2+mux_1)/(lambda+mu),(lambday_2+muy_1)/(lambda+mu))

(x,y)=((1(3)+2(-1))/(1+2),(1(1)+2(4))/(1+2))

(x,y)=(1/3,3)

(a) If (x,y) divides the line joining the point

A(x_1,y_1)=(3,5) and B(x_2,y_2)=(-2,3)

EXTERNALLY in the ratio lambda:mu = 3:2, then;

(x,y)=((lambdax_2-mux_1)/(lambda-mu),(lambday_2-muy_1)/(lambda-mu))

(x,y)=((3(-2)-2(3))/(3-2),((3(3)-2(5))/(3-2))

(x,y)=(-12,-1)