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What is the most precise name for quadrilateral ABCD with vertices A(-3, 2), B(-1, 4), C(4, 4), and D(2, 2)?

parallelogram
rhombus
quadrilateral
rectangle

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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:

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