# .If (3,-1) ,(2,6),(-5,7) are the midpoints of the sides of the triangle ABC, find the area of Triangle ABC.

$if\;midpoint\;of\;any\;triangle\;are\;given\;then\;area\;of\;triangle\;is\;4\;times\\* the\;area\;of\;triangle\;form\;by\;joining\;midpoints\;of\;triangle\\* equation\;of\;DE\;is\;(y-6)=-7(x-2) \Rightarrow 7x+y-20=0\\*Length\;of\; F(-5,7)\;from\;line=\left | \frac{7(-5)+7-20}{\sqrt{49+1}} \right |=\frac{48}{5\sqrt2}\\*DE=\sqrt{(3-2)^2+(-1-6)^2}=5\sqrt2\\* Area\;of\;\triangle ABC=\frac{1}{2}\times 5\sqrt2\times \frac{48}{5\sqrt2}\\* \Rightarrow 24\;sq.\;units\\*So,\;area\;of\;\triangle ABC\;is\;24\;sq.\;units$

## 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/-