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Let O(0,0),P(3,4), and Q(6,0) be the ver...

Let `O(0,0),P(3,4),` and `Q(6,0)` be the vertices of triangle `O P Q` . The point `R` inside the triangle `O P Q` is such that the triangles `O P R ,P Q R ,O Q R` are of equal area. The coordinates of `R` are `(4/3,3)` (b) `(3,2/3)` `(3,4/3)` (d) `(4/3,2/3)`

Text Solution

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As discussed earlier, three medians of a triangle divide the triangle into six equal areas. So point R must be centroid.
Therefore, `R-=((3+6+0)/(3),(4+0+0)/(3))-=(3,(4)/(3))`
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