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Using Coordinates to Prove Geometric Theorems: Mastery Test
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WXYZ is a quadrilateral graphed in the coordinate plane with vertices W(0, 5), X(-3, 2), Y(0,-4), and Z(3,2). What are the lengths of the sides of the quadrilateral,
and what is the correct name for the figure?
The length of XY is about
The length of WX is about
The length of YZ is about
The length of ZW is about
The best name for this quadrilateral is
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Answer :

GinnyAnswer
To find the lengths of the sides of the quadrilateral WXYZ and determine the correct name for the figure, we can use the distance formula in coordinate geometry. 1. Length of XY: - Using the distance formula: √((x2 - x1)² + (y2 - y1)²) - XY = √((0 - 0)² + (-4 - 2)²) = √(0 + 36) = √36 = 6 units 2. Length of WX: - Using the distance formula: √((x2 - x1)² + (y2 - y1)²) - WX = √((0 - (-3))² + (5 - 2)²) = √(3² + 3²) = √(9 + 9) = √18 units (which is about 4.24 units when rounded to two decimal places) 3. Length of YZ: - Using the distance formula: √((x2 - x1)² + (y2 - y1)²) - YZ = √((3 - 0)² + (2 - (-4))²) = √(3² + 6²) = √(9 + 36) = √45 units (which is about 6.71 units when rounded to two decimal places) 4. Length of ZW: - Using the distance formula: √((x2 - x1)² + (y2 - y1)²) - ZW = √((3 - 0)² + (2 - 5)²) = √(3² + (-3)²) = √(9 + 9) = √18 units (which is about 4.24 units when rounded to two decimal places) Therefore, the lengths of the sides of the quadrilateral WXYZ are approximately: - XY = 6 units - WX ≈ 4.24 units - YZ ≈ 6.71 units - ZW ≈ 4.24 units Based on these side lengths, the best name for this quadrilateral is a kite, as it has two distinct pairs of adjacent sides that are equal in length.

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