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Deepak Bora
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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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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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1 Answer

  1. 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 (x1,y1), (x2,y2) and (x3,y3) are

    [(x+ x2+ x3)/3, (y+ y2+ y3)/3]

    (x1,y1) = (-5,3)

    (x2,y2) = (p,-1)

    (x3,y3) = (6,q)

    x co-ordinate of centroid, (x+ x2+ x3)/3 = (-5+p+6)/3 = 1

    p+1 = 3

    p = 3-1

    p = 2

    y co-ordinate of centroid, (y+ y2+ y3)/3 = (3-1+q)/3 = -1

    2+q = 3×-1

    2+q = -3

    q = -3-2

    q = -5

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

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