Answer:
The most precise name for quadrilateral ABCD with vertices A(-3, 2), B(-1, 4), C(4, 4), and D(2, 2) is a parallelogram.
To see why, we can use the slope formula to find the slope of each side of the quadrilateral. If opposite sides of a quadrilateral have the same slope, then it is a parallelogram.
Slope of AB: (4 - 2) / (-1 - (-3)) = 2/2 = 1
Slope of CD: (2 - 4) / (2 - 4) = -2/2 = -1
Slope of BC: (4 - 4) / (-1 - 4) = 0/-5 = 0
Slope of AD: (2 - 2) / (-3 - 2) = 0/-5 = 0
We can see that the slopes of AB and CD are equal, and the slopes of BC and AD are equal. Therefore, ABCD is a parallelogram.
While it is also true that the opposite sides of this parallelogram are equal in length, we cannot say that it is a rhombus because the diagonals are not perpendicular. We also cannot say that it is a rectangle because the angles are not all right angles. Therefore, the most precise name for this quadrilateral is a parallelogram.
Explanation: