Question

Identify whether the points $A(4,2),B(7,5)$ and $C(9,7)$ are collinear or not?

Answer 1

Let the points $(4,2),(7,5)$, and $(9,7)$ be representing the vertices A, B, and C of the given triangle respectively.
Let $A=(4,2)$, $B=(7,5)$ and $C=(9,7)$
AB= $\sqrt{(x_1-x_2{)}^2+(y_1-y_2{)}^2}$
= $\sqrt{(4-7{)}^2+(2-5{)}^2}$ = $\sqrt{18}$

BC = $\sqrt{(7-9{)}^2+(5-7{)}^2}$ = $\sqrt{8}$

AC =$\sqrt{(4-9{)}^2+(2-7{)}^2}$ = $\sqrt{50}$

AB + BC is not equal to AC
Therefore, the points $(4,2),(7,5)$, and $(9,7)$ are not collinear.