Orthocentre of triangle with vertices (0, 0), (3, 4) and (4, 0) is [2003]

Question

Orthocentre of triangle with vertices (0, 0), (3, 4) and (4, 0) is [2003]

Smart Achievers · Accepted Answer

(3)

We know that point of intersection of altitudes of a triangle is the orthocentre of the triangle.

$Equation of altitude A D i.e., line parallel to y-axis through (3, 4) is$

$x = 3 \dots (i)$

$Now, equation of O E ⊥ A B is$

$y = - \frac{3 - 4}{4 - 0} x \Rightarrow y = \frac{x}{4} \dots (i i)$

$Solving (i) and (ii), we get orthocentre as (3, \frac{3}{4})$

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