ICSE Board Question Based on Section Formula Chapter of M.L Aggarwal for class10

In this question given that if two vertices of a parallelogram are (3, 2) ( – 1, 0) and its diagonals meet at (2, – 5), find the other two vertices of the parallelogram.

This is the Question Number 25, Exercise 11 of M.L Aggarwal.

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# If two vertices of a parallelogram are (3, 2) ( – 1, 0) and its diagonals meet at (2, – 5), find the other two vertices of the parallelogram.

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Let A(3,2) and B(-1,0) be the two vertices of the parallelogram ABCD.

Let M(2,-5) be the point where diagonals meet.

Since the diagonals of the parallelogram bisect each other, M is the midpoint of AC and BD.

Consider A-M-C

Let co-ordinate of C be (x

_{2},y_{2})x

_{1}= 3, y_{1}= 2x = 2, y = -5

By midpoint formula, x = (x

_{1}+x_{2})/22 = (3+x

_{2})/23+x

_{2}= 4x

_{2}= 4-3 = 1By midpoint formula, y = (x

_{1}+x_{2})/2-5 = (2+y

_{2})/2-10 = 2+y

_{2}y

_{2}= -10-2 = -12Hence the co-ordinates of the point C are (1,-12).

Consider B-M-D

Let co-ordinate of D be (x

_{2},y_{2})x

_{1}= -1, y_{1}= 0x = 2, y = -5

By midpoint formula, x = (x

_{1}+x_{2})/22 = (-1+x

_{2})/2-1+x

_{2}= 4x

_{2}= 4+1 = 5By midpoint formula, y = (x

_{1}+x_{2})/2-5 = (0+y

_{2})/2-10 = 0+y

_{2}y

_{2}= -10Hence the co-ordinates of the point D are (5,-10).