Question

Find the coordinates of the intersection of the diagonals of parallelogram WXYZ with the following vertices: W (-1, 7), X (8, 7), Y (6, -2) and Z (-3, -2)

A. (1.5, -2)
B. (7, 2.5)
C. (2.5, 2.5)
D. (3.5, 7)

Answer 1

To find the intersection of the diagonals of parallelogram WXYZ, find the midpoints of the diagonals and then find their intersection point.

Step-by-step explanation:

To find the coordinates of the intersection of the diagonals of parallelogram WXYZ, we need to find the midpoint of the line segment connecting points W and Y, and the midpoint of the line segment connecting points X and Z. Then we can find the intersection of these two line segments.

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the formula:

(x1 + x2)/2 , (y1 + y2)/2

Using this formula, we find that the midpoint of WY is (2.5, 2.5), and the midpoint of XZ is (2.5, 2.5). Therefore, the intersection of the diagonals is at the coordinates (2.5, 2.5).

Answer 2

The intersection of the diagonals of a parallelogram is always the midpoint of each of the diagonals, which means all we have to do is grab two opposite vertices and average their coordinates.

Let's use W and Y.

(-1 + 6)/2 = 2.5
(7 + -2)/2 = 2.5

So our point is (2.5,2.5)

We could also use X and Z.
(8 + -3)/2 = 2.5
(7 + -2)/2 = 2.5

Again, we get (2.5,2.5)