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## Answers

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.

...

**given that**

A(0,0), B(1,2), C(x,y)

by the triangle formula -

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

A(0,0), B(1,2), C(x,y)

by the triangle formula -

1/2

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.