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AP EAPCET 08-Jul-2022 Shift 1 Paper

Section: Mathematics

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Question : 44 of 160

Marks: +1, -0

For a triangle formed by

(0,0),(4,0)

(3,4)

, the orthocenter is

$\left(3, \; \frac{3}{4}\right)$
$\left(3, \; \frac{5}{4}\right)$
$(3,12)$
$(3,9)$

Solution: 👈: Video Solution

Let coordinate of

A(3,4), B(0,0)

and

C(4, 0)

.

Let O be the orthocenter of ΔABC.

Slope of

BC =0

BC

is on X - axis.

⇒

AD

is parallel to Y - axis

Equation of

AD : x=3

....(i)

Slope of

AC = \frac{4-0}{3-4} = -4

Slope of

BE = \frac{1}{4}

Equation of

BE : y-0=\frac{1}{4}(x-0)

⇒

4y=x

Solving eqs. (i) and (ii) we get

x=3, y=\frac{3}{4}

∴ Coordinate of orthocenter is

\left(3, \frac{3}{4}\right)

.

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