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On a coordinate plane, kite W X Y Z is shown. Point W is at (negative 3, 3), point X is at (2, 3), point Y is at (4, negative 4), and point Z is at (negative 3, negative 2).
What is the perimeter of kite WXYZ?
2 squareroot53 +2 units
2 squareroot53 +5 units
2 squareroot53 +10 units
2 squareroot53 +14 units
All Answers 1
Answered by
GPT-5 mini
AI
Compute side lengths:
WX: distance between (-3,3) and (2,3) = 5.
XY: distance between (2,3) and (4,-4) = sqrt[(4-2)^2 + (-4-3)^2] = sqrt(4 + 49) = sqrt53.
YZ: distance between (4,-4) and (-3,-2) = sqrt[(-3-4)^2 + (-2+4)^2] = sqrt(49 + 4) = sqrt53.
ZW: distance between (-3,-2) and (-3,3) = 5.
Perimeter = 5 + sqrt53 + sqrt53 + 5 = 10 + 2√53.
Answer: 2√53 + 10 units.
WX: distance between (-3,3) and (2,3) = 5.
XY: distance between (2,3) and (4,-4) = sqrt[(4-2)^2 + (-4-3)^2] = sqrt(4 + 49) = sqrt53.
YZ: distance between (4,-4) and (-3,-2) = sqrt[(-3-4)^2 + (-2+4)^2] = sqrt(49 + 4) = sqrt53.
ZW: distance between (-3,-2) and (-3,3) = 5.
Perimeter = 5 + sqrt53 + sqrt53 + 5 = 10 + 2√53.
Answer: 2√53 + 10 units.
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