Question

The vertices of a triangle are A(10,4) ,B(–4,9) and C(–2, –1). Find the orthocenter.

Answer 1

Answer:

Let perpendiculars drawn from A to BC is AE and from B to AC is BF , thus

AE and BF meet at point P which is the orthocenter of ∆ABC.

Slope of BC=(-1–9)/(-2+4)= -5

Thus ,slope of AE = 1/5.

Equation of AE is:-

y-4= 1/5.(x-10)

or. x-10=5y-20

or. x-5y = -10……………..(1)

Slope of AC =(-1–4)/(-2–10)= 5/12.

Slope of BF =-12/5.

Equation of BF is:-

y-9=-12/5.(x+4).

or 5y-45=-12x-48

or. 12x+5y= -3………………..(2)

from eqn (1) and (2).

x/(15+50)=y/(-120+3)= -1/(5+60)

x/65=y/-117 =-1/65.

x=-65/65= -1.

y= 117/65 = 9/5.

Coordinates of the orthocenter = (-1 ,9/5).

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