An equilateral triangle whose orthocentre is $(3, - 2)$ , one side is on x-axis vertex of triangle which is not on $x$ -axis is

(3, - 6)

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(1, - 2)

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(9, - 2)

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(3, - 3)

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Solution

The correct option is A $(3, - 6)$
$M = (3, 0)$
$O = (3, - 2)$
$O M = 2$
$I n e q u i l a t e r a l Δ$
$\frac{A O}{O M} = \frac{2}{1}$
$\Rightarrow A O = 2 O M$
$= 2 \times 2$
$= 4$
$∴ A M = A O + O M$
$= 4 + 2 = 6$
$H e n c e A (3, - 6)$

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An equilateral triangle whose orthocentre is (3,−2), one side is on x-axis vertex of triangle which is not on x-axis is

The correct option is A (3,−6) M=(3,0) O=(3,−2) OM=2 InequilateralΔ AOOM=21 ⇒AO=2OM =2×2 =4 ∴AM=AO+OM =4+2=6 HenceA(3,−6)

An equilateral triangle whose orthocentre is $(3, - 2)$ , one side is on x-axis vertex of triangle which is not on $x$ -axis is

The correct option is A $(3, - 6)$
$M = (3, 0)$
$O = (3, - 2)$
$O M = 2$
$I n e q u i l a t e r a l Δ$
$\frac{A O}{O M} = \frac{2}{1}$
$\Rightarrow A O = 2 O M$
$= 2 \times 2$
$= 4$
$∴ A M = A O + O M$
$= 4 + 2 = 6$
$H e n c e A (3, - 6)$