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Problem 20

The vertices of a triangle are $$(0,3),(-3,0)$$ and $$(3,0)$$. The co-ordinates of its orthocentre are: (a) $$(0,-2)$$ (b) $$(0,2)$$ (c) $$(0,3)$$ (d) $$(0,-3)$$

Expert verified
The orthocentre of the triangle is point (c) $$(0,3)$$.
See the step by step solution

Step 1: Identify the Type of the Triangle

Check the coordinates of the vertices and identify the type of the triangle. Here, $$(0,3),(-3,0)$$ and $$(3,0)$$ form a right triangle.

Step 2: Locate the Orthocentre for a Right Triangle

Recall that for a right triangle, the orthocentre is the vertex forming the right angle. Here, the point $$(0,3)$$ must be the orthocentre.

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