Question

✨ here is your question -

➡ Find the orthocenter of the triangle whose vertices are (0,0),(3,0) and (0,4).

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Answer 1

Well, the orthocenter of a triangle is the point where all the possible altitudes of the triangle intersect each other.

Means, if we draw corresponding altitudes to the three sides of a triangle, to the opposite vertices, then they meet at a common point, and that point is the orthocenter.

But what about if the triangle is a right angled one?

A right triangle, say ∆ABC, has two perpendicular sides, say a, b, so that their altitudes are b and a respectively, which pass through the right angled vertex. Since the altitude of the hypotenuse, say c, also passes through the right angled vertex, that vertex is the orthocenter.

Here we're actually given a right triangle whose sides have lengths 3 units, 4 units and 5 units.

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\put(0,0){\line(1,0){30}}\put(0,0){\line(0,1){40}}\put(30,0){\line(-3,4){30}}\put(-3,-4){ (0,0) }\put(-3,43){ (0,4) }\put(30,-4){ (3,0) }\end{picture}$

Here the triangle is right angled at the point (0, 0), i.e., the origin, so the origin is the orthocenter.

Answer 2

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Solution