If `(1,4)` is the centroid of a triangle and the coordinates of its any two vertices are `(4,-8)` and `(-9,7),` find the area of the triangle.
If `(1,4)` is the centroid of a triangle and the coordinates of its any two vertices are `(4,-8)` and `(-9,7),` find the area of the triangle.
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Correct Answer - `166.5` sq.unit
Let the given triangle be ABC.
centroid is `G(1,3)` and two vertices of triangle are `B(4,-8)` and `C(-9,7)`
`"Area of triangle GBC"=(1)/(2)||{:(1,,4),(4,,-8),(-9,,7),(1,,4):}||`
`=(1)/(2)|[-8-16+28-72-36-7]|`
`=555` sq.units.
Hence, area of triangle `ABC=3xx55.5=166.5`sq.units
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