This question is Based on Section Formula Chapter of M.L Aggarwal book for ICSE BOARD for class 10.

Here you have given two vertices of a triangle. Find the third vertex for which centroid is also given.

This is the Question Number 35, Exercise 11 of M.L Aggarwal.

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# Two vertices of a triangle are (3, – 5) and ( – 7, 4). Find the third vertex given that the centroid is (2, – 1).

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Given (x

_{1},y_{1}) = (3,-5)(x

_{2},y_{2}) =(-7,4)Co-ordinates of centroid are (2,-1)Co-ordinates of the centroid of a triangle, whose vertices are (x

_{1},y_{1}), (x_{2},y_{2}) and (x_{3},y_{3}) are[(x_{1 }+ x_{2}+ x_{3})/3, (y_{1 }+ y_{2}+ y_{3})/3](x_{1 }+ x_{2}+ x_{3})/3 = (3+-7+x_{3})/3 = 2 [x co-ordinate of centroid]-4+x

_{3}= 2×3-4+x

_{3}= 6x

_{3}= 6+4x

_{3}= 10(y

_{1 }+ y_{2}+ y_{3})/3 = -1 [y co-ordinate of centroid]-5+4+y

_{3}= -1×3-1+y

_{3}= -3y

_{3}= -3+1y

_{3}= -2Hence the third vertex is (10,-2).