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?

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Answer 1 · 2015-09-19T03:23:50

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

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

(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)#