Class 10

Math

All topics

Coordinate Geometry

Show that the following points are collinear.

$A(−5,1),B(5,5)$ and $C(10,7)$.

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

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

$A(−5,1),B(5,5)$ and $C(10,7)$

$Δ=21 {5−(5−7)+5(7−1)+10(1−5)}$

$Δ=21 {10+30−40}$

$Δ=0$

Hence points are collinear.