# Show that (3,2),(2,-3),(0,0) are the vertices of a right angled triangle using distance formula

Assinging the points:-
$(x_{1},y_{1})=(3,2)$
$(x_{2},y_{2})=(2,-3)$
$(x_{3},y_{3})=(0,0)$
$\therefore$ Distance between two points=$\sqrt{(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}$
AB=$\sqrt{(2-3)^{2}+(-3-2)^{2}}=\sqrt{1+25}=\sqrt{26}\, units$
BC=$\sqrt{(0-2)^{2}+(0+3)^{2}}=\sqrt{4+9}=\sqrt{13}\, units$
CA=$\sqrt{(0-3)^{2}+(0-2)^{2}}=\sqrt{9+4}=\sqrt{13}\, units$
$(\sqrt{13})^{2}+(\sqrt{13})^{2}=(\sqrt{26})^{2}$
$\therefore BC^{2}+CA^{2}=AB^{2}$
Hence the given points form a right angled traingle.

## Most Viewed Questions

### Preparation Products

##### Knockout JEE Main (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
##### Knockout JEE Main (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-
##### Knockout NEET (Six Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 9999/- ₹ 8499/-
##### Knockout NEET (Nine Month Subscription)

- AI Coach Study Modules, - Unlimited Mock Tests, - Study Improvement Plan.

₹ 13999/- ₹ 12499/-