The fourth vertex D of a parallelogram ABCD whose three vertices are A( - 2, 3), B(6, 7) and C(8, 3) is

Given a parallelogram ABCD whose three vertices are;

A ( - 2, 3),

B (6, 7) and

C (8, 3)

Let the fourth vertex of parallelogram, D = (x_{4}, y_{4}) and L, M be the middle points of AC and BD, respectively

L =

Since, mid - point of a line segment having points (x_{1}, y_{1}) and (x_{2}, y_{2})

= and

M =

As we know ABCD is a parallelogram, therefore diagonals AC and BD will bisect each other.

So, L and M are the same points

3 = and

3 =

→ 6 = 6 + x_{4} and 6 = 7 + y_{4}

→ x_{4} = 0 and y_{4} = 6 – 7

∴ x_{4} = 0 and y_{4} = - 1

Hence, the fourth vertex of parallelogram is D = (x4, y4) = (0, 1)

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