A 4-4- B 3-5 and C -1-1 are the vertices ofA- an equilateral triangleB- a right angled triangleC- an isosceles triangleD- None of these

The correct option is B a right angled triangleIn Δ ABC m_1= slope of AB=5 43 4= 1 m_2= slope of AC= 1 4 1 4=1 m_3= slope of BC=5+13+1=32 Clearly, m_1m_2= 1. ∴ ...

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Byju's Answer

Standard XII

Mathematics

Condition for Two Lines to Be Parallel

A 4,4, B 3,5 ...

Question

$A (4, 4), B (3, 5)$ and $C (- 1, - 1)$ are the vertices of

an equilateral triangle

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a right angled triangle

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an isosceles triangle

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None of these

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Solution

The correct option is B a right angled triangle
In $Δ A B C$
$m_{1} =$ slope of $A B = \frac{5 - 4}{3 - 4} = - 1$
$m_{2} =$ slope of $A C = \frac{- 1 - 4}{- 1 - 4} = 1$
$m_{3} =$ slope of $B C = \frac{5 + 1}{3 + 1} = \frac{3}{2}$
Clearly, $m_{1} m_{2} = - 1$ .
$∴ A B ⊥ A C$ ie.,
$∠ C A B = \frac{π}{2}$
Hence, the given points are the vertices of a right angled triangle.

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The correct option is B a right angled triangleIn ΔABC m1= slope of AB=5−43−4=−1 m2= slope of AC=−1−4−1−4=1 m3= slope of BC=5+13+1=32 Clearly, m1m2=−1. ∴AB⊥AC ie., ∠CAB=π2 Hence, the given points are the vertices of a right angled triangle.

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