A triangle having vertices as A 4-4- B 3-5 and C -1-1 will beA- Right angled at AB- Right angled at CC- Right angled at BD- Not a right angled triangle

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Byju's Answer

Standard XII

Mathematics

Condition for Two Lines to Be Perpendicular

A triangle ha...

Question

A triangle having vertices as $A (4, 4), B (3, 5)$ and $C (- 1, - 1)$ will be

Right angled at

A

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Right angled at

B

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Right angled at

C

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Not a right angled triangle

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Solution

The correct option is A Right angled at $A$
Let $m_{1}, m_{2}$ and $m_{3}$ be the slopes of $A B, A C$ and $B C$ respectively, then
$m_{1} =$ Slope of line $A B = \frac{5 - 4}{3 - 4} = - 1$
$m_{2} =$ Slope of line $A C = \frac{- 1 - 4}{- 1 - 4} = 1$
$m_{3} =$ Slope of line $B C = \frac{- 1 - 5}{- 1 - 3} = \frac{3}{2}$
Clearly we can see that
$m_{1} m_{2} = - 1$
So, it is a right angled triangle having right angle at $A .$

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