Question

Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (-2, -1), (1, 0), (4, 3) and (1, 2) meet.

Answer 1

The coordinates of the point where the diagonals of the parallelogram meet is (1, 1)

Consider the attached diagram while going through the following steps.

Given,

the coordinates of the sides of parallelogram are

A = (-2, -1), B = (1, 0), C = (4, 3) and D = (1, 2)

Then, we have, the diagonals AC and AD.

Let the coordinates of the point where the diagonals of the parallelogram meet be O(x, y).  

As we know that the diagonals of a parallelogram bisect each other.

Therefore, we have,

∴ (x, y) = (A + C) / 2 = [(-2+4)/2 , (-1+3)/2] = (2/2 , 2/2) = (1, 1)

OR

∴ O(x, y) = (B + D) / 2 = [(1+1)/2 , (0+2)/2] = (2/2 , 2/2) = (1, 1)

Therefore, the coordinates of the point where the coordinates of the diagonal meet is (1, 1)

Answer 2

Answer:

Answer is (1,1)

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