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.
Deepak BoraNewbie
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.
x1 = 1, y1 = 2
x2 = 4, y2 = 0
By midpoint formula, x = (x1+x2)/2
x = (1+4)/2 = 5/2
By midpoint formula, y = (y1+y2)/2
y = (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.
x1 = 1, y1 = 0
x = 5/2, y = 1
By midpoint formula, x = (x1+x2)/2
5/2 = (1+x2)/2
5 = 1+x2
x2 = 5-1 = 4
By midpoint formula, y = (y1+y2)/2
1 = (0+y2)/2
1 = y2/2
y2 = 2
Hence the co-ordinates of D are (4,2).