Question

the line segment joining a(1, -1),b (3,1) is extended to c . if 2bc=3ab find the co-ordinates of c

Answer 1

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Answer 2

given 2BC = 3AB

distance of AB by distance formula is

$2 \sqrt{2}$

then BC=

$3 \sqrt{3}$

let C be x,y

then tangent if line is 1=(y-1)/(x-3)=(y+1)/(x-1)

which gives relation x=y+2

equation 1

BC square is 18

BC square is also square of (x-3) + square of (y-1) = 18

equation 2

by solving we get (square of x) + (square of y) - (6 multiply by x) - (2 multiply by y) = 8

now by solving equation 1 and 2 we get coordinates of c is (6,4) or (0,-2)