Geometry

Quadrilaterals

Medium

If A (1, 2), B(4, y), C(x, 6) and D(3, 5) are the vertices of a parallelogram ABCD, then find the values of x and y.

$x=3, y=6$

$x=6, y=3$

$x=0, y=0$

$x=0, y=1$

✅ Correct Option: 2

In a parallelogram ABCD, diagonals AC and BD bisect each other, so midpoint of AC equals midpoint of BD. Midpoint of AC: $\left(\frac{1+x}{2}, \frac{2+6}{2}\right)$ . Midpoint of BD: $\left(\frac{4+3}{2}, \frac{y+5}{2}\right)$ . Equating x-coords: $\frac{1+x}{2} = \frac{7}{2}$ , so $x=6$ . Equating y-coords: $\frac{8}{2} = \frac{y+5}{2}$ , so $y=3$ .

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If A (1, 2), B(4, y), C(x, 6) and D(3, 5) are the vertices of a parallelogram ABCD, then find the values of x and y.

Solution

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