The parallelogram PQRS has vertices P( -2, 3), Q(1, 4), R(2, 6) and S(-1, 5). Find the coordinates of the point of intersection of the diagonals.
The diagonals bisect each other; hence, the point of intersection is a midpoint M(x, y)
Considering diagonal \(\overline{PR}\), P(-2, 3) and R(2, 6)
The midpoint of a line M(x, y) is given as x = \(\frac{x_1 + x_2}{2}\), y = \(\frac{y_1 + y_2}{2}\)
x = \(\frac{x_1 + x_2}{2}\) = \(\frac{-2 + 2}{2}\) = \(\frac{0}{2}\) = 0
y = \(\frac{y_1 + y_2}{2}\) = y = \(\frac{3 + 6}{2}\) = \(\frac{9}{2}\) = 4\(\frac{1}{2}\)
The coordinate of intersection M = (0, 4\(\frac{1}{2}\))
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