The vertices of quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). The quadrilateral is a Blank 1 Question 46

To determine the type of the quadrilateral ABCD, we can calculate the slopes of the sides AB, BC, CD, and DA.

The slope of a line segment with endpoints (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1).

1. Calculate the slope of AB: Slope of AB = (5-0) / (4-0) = 5/4

2. Calculate the slope of BC: Slope of BC = (9-5) / (9-4) = 4/5

3. Calculate the slope of CD: Slope of CD = (4-9) / (5-9) = -5/4

4. Calculate the slope of DA: Slope of DA = (0-4) / (0-5) = 4/5

From the above calculations, we can see that the slopes of AB and CD are negative reciprocals of each other, and the slopes of BC and DA are the same. This means that AB is parallel to CD and BC is parallel to DA.

Therefore, the quadrilateral ABCD is a parallelogram.