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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.

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(1, 1)

(1, 3)

(5, 1)

None of these

answer is A.

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Detailed Solution

Given the coordinates of parallelogram.
Let the vertices of parallelogram in order are

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

.
So, the diagonals will be

AC

and

BD

.
Since the diagonals of a parallelogram bisects each other, so midpoint of

AC

BD

will be the intersection point of diagonals.
Midpoint of two point

{(x}_{1}, y_{1})

{(x}_{2}, y_{2})

is ,

(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2})

.
Hence by mid-point theorem, midpoint of

AC

where

A (- 2, - 1) and C (4, 3)

x = \frac{- 2 + 4}{2}

\Rightarrow x = 1

And,

y = \frac{- 1 + 3}{2}

\Rightarrow y = 1

Thus, the coordinates of the required point is

(1, 1)

.
Therefore, option (1) is correct.

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