The orthocenter of the triangle formed by (0, 0), (8, 0) and (4, 6) is

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Question

The orthocenter of the triangle formed by (0, 0), (8, 0) and (4, 6) is

Options:

A . 4,83

B . 3,4

C . 4,3

D . −3,4

Answer: Option A
:
A
Sol: Let A ≡ (0, 0), B ≡ (8, 0) and C ≡ (4, 6).

The Orthocenter Of The Triangle Formed By (0, 0), (8, 0) And...

Slope of BC =

\frac{6 - 0}{4 - 0} = \frac{3}{2}

Equation of the line through A(0, 0) and perpendicular to BC is
(y – 0) =

\frac{2}{3}

(x – 0) i.e. 2x – 3y = 0 …… (1)
Slope of CA =

\frac{6 - 0}{4 - 0} = \frac{3}{2}

Equation of the line through B(8, 0) and perpendicular to CA is
(y – 0) =

- \frac{2}{3}

(x – 8) i.e., 2x + 3y = 16 …… (2)
Solving (1) and (2), the orthocenter is

4, \frac{8}{3}

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