Question

The diagonals of parallelogram BEND intersect at point Q. What are the coordinates of point Q given the coordinates of the vertices of the parallelogram:

B(-4, 7), E(3, 0), N(2, -5), and D(-5, 2).

Answer 1

The coordinates of point Q, the intersection of the diagonals of parallelogram BEND, are (-1/2, 1/2).

Step-by-step explanation:

To find the coordinates of the intersection point Q, we can use the midpoint formula. The midpoint of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by ((x₁ + x₂)/2, (y₁ + y₂)/2).

For the diagonal BD, the endpoints are B(-4, 7) and D(-5, 2). The midpoint of BD is ((-4 + (-5))/2, (7 + 2)/2) = (-9/2, 9/2). Similarly, for diagonal EN with endpoints E(3, 0) and N(2, -5), the midpoint is ((3 + 2)/2, (0 + (-5))/2) = (5/2, -5/2).

Now, the coordinates of point Q are the midpoint of the line segment connecting the midpoints of the diagonals BD and EN. Therefore, Q is at ((-9/2 + 5/2)/2, (9/2 + (-5/2))/2) = (-1/2, 1/2).

In conclusion, the coordinates of point Q, the intersection of the diagonals of parallelogram BEND, are (-1/2, 1/2). This point represents the center of symmetry for the parallelogram.