Question

if the point (0,0),(1,2)and (x,y) are collinear then find the relationship b/w x amd y

Answer 1

Slope of line = (0-2)/(0-1) = (-2)/(-1) = 2
Since (x,y) also lies on that line

Slope of line = (y-2)/(x-1)
=> 2(x-1) = y-2
=> 2x-2 = y-2
=> y = 2x
... is the relation between x and y.

Answer 2

given that

A(0,0), B(1,2), C(x,y)

by the triangle formula -

1/2 Ι x₁(y₂-y₃)+x₂(y₃-y₁)+x₃(y₁-y₂) Ι=0

then,

1/2 Ι 0(2-y)+1(y-0)+x(0-2) Ι = 0

1/2 Ι 0+y+2x Ι = 0

1/2 Ι 2x+y Ι = 0

2x+y = 0

hence proved

note: in the above this symbol ' Ι ' means modules.