Assertion :The points $A \equiv (- 2, 2)$ , $B \equiv (2, - 2)$ and $C \equiv (1, 1)$ are the vertices of an obtuse angled isosceles. Reason: Every obtuse angled triangle is isosceles.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is C Assertion is correct but Reason is incorrect
Reason is not correct as the triangle with angle $120^{\circ}, 40^{\circ}, 20^{\circ}$ is obtuse angled but not isosceles.
In assertion $A B = 4 \sqrt{2}, A C = \sqrt{10}, B C = \sqrt{10}$
$cos C = \frac{A C^{2} + B C^{2} - A B^{2}}{2 (A C) (B C)} = \frac{10 + 10 - 32}{2 \times \sqrt{10} \sqrt{10}} < 0$
$\Rightarrow$ C is obtuse.
So the triangle is obtuse angled isosceles.

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Assertion :The points A≡(−2,2), B≡(2,−2) and C≡(1,1) are the vertices of an obtuse angled isosceles. Reason: Every obtuse angled triangle is isosceles.

Assertion :The points $A \equiv (- 2, 2)$ , $B \equiv (2, - 2)$ and $C \equiv (1, 1)$ are the vertices of an obtuse angled isosceles. Reason: Every obtuse angled triangle is isosceles.