Question

Show that $(-2,3),(8,3)$ and $(6,7)$ are the vertices of a right angled triangle.

Answer 1

Let $A=(-2,3),B=(8,3)$ and $C=(6,7).$

By using distance formula,

$A{B}^2=(8-(-2){)}^2+(3-3{)}^2$

$=(10{)}^2+(0{)}^2$

$=100$

$B{C}^2=(6-8{)}^2+(7-3{)}^2$

$=(-2{)}^2+(4{)}^2$

$=20$

$A{C}^2=(6-(-2){)}^2+(7-3{)}^2$

$=(8{)}^2+(4{)}^2$

$=80$

$A{B}^2=A{C}^2+B{C}^2$

Hence, by the converse of the Pythagoras theorem, we can say that $△ABC$ is a right-angled triangle.