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.
Deepak BoraNewbie
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 (x1,y1) = (3,-5)
(x2,y2) = (-7,4)
Co-ordinates of centroid are (2,-1)
Co-ordinates of the centroid of a triangle, whose vertices are (x1,y1), (x2,y2) and (x3,y3) are
[(x1 + x2+ x3)/3, (y1 + y2+ y3)/3]
(x1 + x2+ x3)/3 = (3+-7+x3)/3 = 2 [x co-ordinate of centroid]
-4+x3 = 2×3
-4+x3 = 6
x3 = 6+4
x3 = 10
(y1 + y2+ y3)/3 = -1 [y co-ordinate of centroid]
-5+4+y3 = -1×3
-1+y3 = -3
y3 = -3+1
y3 = -2
Hence the third vertex is (10,-2).