Question

Find the relation between x and y if the points A(x,y), B(-5,7) and C(-4,5) are collinear.

Answer 1

Given that the points A(x,y) ,B(-5,7) and C(-4,5) are collinear.

So, the area of triangle formed by their vertices is 0.

Therefore,

$\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]=0$

$\Rightarrow \frac{1}{2}\left[x\right(7-5)-5(5-y)-4(y-7\left)\right]=0$

$\Rightarrow \frac{1}{2}\left[x\right(2)-5(5-y)-4(y-7\left)\right]=0$

$\Rightarrow 2x-25+5y-4y+28=0$

$\Rightarrow 2x+y+3=0$

$y=-2x-3$

which is the required relation between x and y i.e., $y=-2x-3$.