Questions and answers

Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (– 2, 8)

Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (– 2, 8)

by Anil Sharma -
Number of replies: 0
Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (– 2, 8), respectively. Then, the coordinates of the vertex D are:
(1) (– 4, 5)
(2) (4, 5)
(3) (– 3, 4)
(4) (0, 11)


SOLUTION: We know that diagonals of a parallelogram intersect at midpoint, therefore midpoint of A and C will be the same as that of B and D. Let the point D is \((x,y)\)
\(\left( {\frac{{1 - 2}}{2},\,\frac{{1 + 8}}{2}} \right) = \left( {\frac{{x + 3}}{2},\,\frac{{y + 4}}{2}} \right)\)
\( \Rightarrow x =  - 4,\,\,y = 5\)