Question

show that the point(-5,1), (1-1),(1,-2) are collinear can someone solve and answer​

Answer 1

$Let \: A(-5,1), B(1,-1) \:and \:C(1,-2) \: are$

$vertices \: of \: \triangle ABC$

$Here , x_{1} = -5 , y_{1} = 1 ;$

$x_{2} = 1 , y_{2} = -1 ;$

$and \: x_{3} = 1 , y_{3} = -2 ;$

$\blue{ Area \: of \: \triangle ABC}$

$\blue{= \frac{1}{2}|x_{1}(y_{2}-y_{3})+x_{2}(y_{3}-y_{1})+x_{3}(y_{1}-y_{2})|}$

$= \frac{1}{2}|(-5)(-1+2)+1(-2-1)+1(1+1)|$

$= \frac{1}{2}| -5-3+2|$

$= \frac{1}{2} |-6|$

$= \frac{1}{2} \times 6$

$= 3$

$\neq 0$

$\green { A,B , C \: are \: non \: collinear }$

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