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Question
Write the coordinates of the orthocentre of the triangle formed by points (8, 0), (4, 6) and (0, 0).
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Solution
The intersection point of three altitudes of a triangle is called orthocentre.
In the figure, two altitudes ON and BM of ∆OAB are shown.
Slope of AB = \[\frac{6 - 0}{4 - 8} = - \frac{3}{2}\]
\[\therefore\] Slope of ON \[= \frac{2}{3} \left( \because \text{ Product of slopes }= - 1 \right)\]
Equation of ON:
\[\left( y - 0 \right) = \frac{2}{3}\left( x - 0 \right)\]
\[y = \frac{2}{3}x\] ... (1)
Equation of BM:
x = 4 ... (2)
On solving equations (1) and (2), we get
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