Question:
If the axes are translated to the orthocentre of the triangle formed by points \(A(7,5), B(-5,-7), C(7,-7)\), then the coordinates of the incentre of the triangle in the new system are?
If the axes are translated to the orthocentre of the triangle formed by points \(A(7,5), B(-5,-7), C(7,-7)\), then the coordinates of the incentre of the triangle in the new system are?
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Use translation of coordinate axes by subtracting orthocentre coordinates from point coordinates to get new system values.
Updated On: Jun 6, 2025
- \((-6,6)\)
- \(\left(\frac{5}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)\)
- \(\left(\frac{-12}{2+\sqrt{2}}, \frac{12}{2+\sqrt{2}}\right)\)
- \(\left(-5\sqrt{2}, -7\sqrt{2}\right)\)
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The Correct Option is C
Solution and Explanation
Find orthocentre \(H\) by solving altitudes of \(\triangle ABC\). Translate axes so \(H\) becomes origin. Coordinates of incentre \(I\) in old axes are adjusted by subtracting \(H\). This yields new coordinates of incentre as \(\left(\frac{-12}{2+\sqrt{2}}, \frac{12}{2+\sqrt{2}}\right)\).
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