Class 10

Math

All topics

Coordinate Geometry

Show that the following points are collinear.

$A(5,1),B(1,−1)$ and $C(11,4)$.

Points are collinear if the area of a triangle is equal to zero.

Area of $ΔABC=21 [x_{1}(y_{2}−y_{3})+x_{2}(y_{3}−y_{1})+x_{3}(y_{1}−y_{2})]$

$A(5,1),B(1,−1)$ and $C(11,4)$

$Δ=21 {5(−1−4)+1(4−1)+11(1+1)}$

$=21 {−25+3+22}$

$=0$

Hence points are collinear.