An Important Question of M.L Aggarwal book of class 10 Based on Section Formula Chapter for ICSE BOARD.

The vertices of a triangle are given. Find the values asked if the centroid point of the triangle is given.

This is the Question Number 36, Exercise 11 of M.L Aggarwal.

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# The vertices of a triangle are A ( – 5, 3), B (p, – 1) and C (6, q). Find the values of p and q if the centroid of the triangle ABC is the point (1, – 1).

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Given vertices of the triangle are A(-5,3), B(p,-1) and C(6,q).Co-ordinates of centroid are (1,-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},y_{1}) =(-5,3)(x

_{2},y_{2}) =(p,-1)(x

_{3},y_{3}) =(6,q)x co-ordinate of centroid, (x_{1 }+ x_{2}+ x_{3})/3 = (-5+p+6)/3 = 1p+1 = 3

p = 3-1

p = 2

y co-ordinate of centroid,(y_{1 }+ y_{2}+ y_{3})/3 = (3-1+q)/3 = -12+q = 3×-1

2+q = -3

q = -3-2

q = -5

Hence the value of p and q are 2 and -5 respectively.