Question

The three consecutive vertices of a parallelogram (-2,1) (1,0) (4,3). Find the co-ordinates of the fourth vertex
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Answer 1

Answer:

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Answer 2

Answer:

[1, 4]

Step-by-step explanation:

Let ABCD be the parallelogram where A, B and C are respectively (-2, 1), (1, 0) and (4, 3) and D is unknown.

Construction - Join AC and BD and let them intersect at a point O

Solution:

Since ABCD is a parallelogram, AC and BD bisect each other. [Property of the diagonals of a parallelogram]

The two dioganals bisect each other at O.

=> Mid-point of AC = Mid-point of BD

Then, by Mid-point formula:

$[\frac{x_{A} + x_{C}}{2} , \frac{y_{A} + y_{C}}{2}] = [\frac{x_{B} + x_{D}}{2} , \frac{y_{B} + y_{D}}{2}]$

=> $[\frac{-2 + 4}{2} , \frac{1 + 3}{2}] = [\frac{1 + x_D}{2} , \frac{0 + y_D}{2} ]$

=> $[\frac{2}{2} , \frac{4}{2}] = [\frac{1 + x_D}{2} , \frac{y_D}{2} ]$

=> $[2, 4] = [1 + x_D , y_D]$          [2 cancelled from both sides]

=> $x_D = 2 - 1$     and      $y_D = 4$

=> $D = [1, 4]$