If $(2, 4), (4, 2)$ are the extremities of the hypotenuse of right angled isosceles triangle, then the third vertex is

(2, 2) o r (4, 4)

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(3, 3) o r (4, 4)

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(2, 2) o r (3, 3)

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(2, 3) o r (3, 2)

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Solution

The correct option is D $(2, 2) o r (4, 4)$
Length of Hypotenuse $= \sqrt{(2 - 4)^{2} + (4 - 2)^{2}} = 2 \sqrt{2}$

Since, it is an Isosceles Triangle , Let us Assume its height and base $= a$
such that $\sqrt{a^{2} + a^{2}} = 2 \sqrt{2} \Rightarrow a \sqrt{2} = 2 \sqrt{2} \Rightarrow a = 2$

From Given options only (2,2) and (4,4) are satisfying this Equation
$\sqrt{(x - 2)^{2} + (y - 4)^{2}} = 2$

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If (2,4),(4,2) are the extremities of the hypotenuse of right angled isosceles triangle, then the third vertex is

The correct option is D (2,2) or (4,4)Length of Hypotenuse =√(2−4)2+(4−2)2=2√2Since, it is an Isosceles Triangle , Let us Assume its height and base =asuch that √a2+a2=2√2⇒a√2=2√2⇒a=2From Given options only (2,2) and (4,4) are satisfying this Equation√(x−2)2+(y−4)2=2

If $(2, 4), (4, 2)$ are the extremities of the hypotenuse of right angled isosceles triangle, then the third vertex is