Question

Find the coordinates of the intersection of the diagonals
of parallelogram XYZW with vertices X(2, 2), Y(3, 6), Z(10, 6), and W(9,2). Hint: what do we know about
the diagonals of a parallelogram?

Answer 1

Answer:

We know the basic facts about parallelogram is The basic formula for calculating the area of a parallelogram is the length of one side times the height of the parallelogram to that side.

Step-by-step explanation:

Answer 2

The coordinates of the intersection of the diagonals  of parallelogram XYZW is at (6, 4).

Parallelogram

A parallelogram is a quadrilateral in which opposite sides are parallel and equal. The diagonals of a parallelogram bisect each other.

Given parallelogram XYZW with vertices X(2, 2), Y(3, 6), Z(10, 6), and W(9,2).

The equation of diagonal XZ is:

• $y-2=\frac{6-2}{10-2} (x-2)\\\\y=0.5x+1$

The equation of diagonal YW is:

• $y-6=\frac{2-6}{9-3} (x-3)\\\\y=-\frac{2}{3} x+8$

The point of intersection is at:

0.5x + 1 = (-2/3)x + 8

x = 6. Hence y = 4

The coordinates of the intersection of the diagonals  of parallelogram XYZW is at (6, 4).

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