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

Here you have to find the third vertex of a triangle if its two vertices are given and midpoint of one sides is also given in the question.

This is the Question Number 27, Exercise 11 of M.L Aggarwal.

Deepak BoraNewbie

# Find the third vertex of a triangle if its two vertices are ( – 1, 4) and (5, 2) and midpoint of one sides is (0, 3).

Share

Let A

(-1,4) and B(5,2) are the vertices of the triangle and let D(0,3) is the midpoint of side AC.Let co-ordinate of C be (x,y).Consider D(0,3) as midpoint of ACBy midpoint formula,(-1+x)/2 = 0-1 +x = 0x = 1By midpoint formula,(4+y)/2 = 34+y = 6y = 6-4 = 2So the co-ordinates of C are (1,2).Consider D(0,3) as midpoint of BCBy midpoint formula,(5+x)/2 = 05 +x = 0x = -5By midpoint formula,(2+y)/2 = 32+y = 6y = 6-2 = 4So the co-ordinates of C are (-5,4).Hence the co-ordinates of the point C will be (1,2) or (-5,4).