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

Here three consecutive vertices of a parallelogram ABCD are given. Find the fourth vertex D.

This is the Question Number 23, Exercise 11 of M.L Aggarwal.

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# Three consecutive vertices of a parallelogram ABCD are A (1, 2), B (1, 0) and C (4, 0). Find the fourth vertex D.

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Let M be the midpoint of the diagonals of the parallelogram ABCD.

Co-ordinate of M will be the midpoint of diagonal AC.

Given points are

A(1,2), B(1,0) and C(4,0).Consider line AC.x

_{1 }= 1, y_{1}= 2x

_{2 }= 4, y_{2}= 0By midpoint formula, x = (x

_{1}+x_{2})/2x = (1+4)/2 = 5/2

By midpoint formula, y = (y

_{1}+y_{2})/2y = (2+0)/2 = 2/2 = 1

Hence the co-ordinates of M are (5/2,1).

M is also the midpoint of diagonal BD.

Consider line BD and M as midpoint.

x

_{1 }= 1, y_{1}= 0x

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

_{1}+x_{2})/25/2 = (1+x

_{2})/25 = 1+x

_{2}x

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

_{1}+y_{2})/21 = (0+y

_{2})/21 = y

_{2}/2y

_{2}= 2Hence the co-ordinates of D are (4,2).