Question

Show that the points A(4,2) B(7,5) C(9,7) are collinear.

Answer 1

Three points $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ collinear if $x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=0$

$\therefore$ For $A(4,2)$ $B(7,5)$ $C(9,7)$

$4(5-7)+7(7-2)+9(2-5)$

$=(4\times -2)+(7\times 5)+(9\times (-3))$

$=-8+35+(-27)$

$=27-27$

$=0$

$\therefore$ $A(4,2)$, $B(7,5)$ and $C(9,7)$ are collinear.