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# 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).

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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.

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1.  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 AC

By midpoint formula,

(-1+x)/2 = 0

-1 +x = 0

x = 1

By midpoint formula,

(4+y)/2 = 3

4+y = 6

y = 6-4 = 2

So the co-ordinates of C are (1,2).

Consider D(0,3) as midpoint of BC

By midpoint formula,

(5+x)/2 = 0

5 +x = 0

x = -5

By midpoint formula,

(2+y)/2 = 3

2+y = 6

y = 6-2 = 4

So the co-ordinates of C are (-5,4).

Hence the co-ordinates of the point C will be (1,2) or (-5,4).

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