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Question: The orthocentre of the triangle with vertices (–2, –6), (–2, 4) and (1, 3) is...

The orthocentre of the triangle with vertices (–2, –6), (–2, 4) and (1, 3) is

A

(–3, 1)

B

(–1, 1/3)

C

(1, 3)

D

None of these

Answer

(1, 3)

Explanation

Solution

Let A (–2, –6) B(–2, 4) and C(1, 3)

AB = (–2+2)2+(4+6)2\sqrt{(–2 + 2)^{2} + (4 + 6)^{2}} = 10

BC = (1+2)2+(3−4)2\sqrt{(1 + 2)^{2} + (3 - 4)^{2}} = 10\sqrt{10}

CA = (−2−1)2+(−6−3)2\sqrt{( - 2 - 1)^{2} + ( - 6 - 3)^{2}} = 90\sqrt{90}

(AB)2 = (BC)2 + (CA)2

Right angle at C

Ž orthocentre (1, 3)