Asked by A
On a coordinate plane, parallelogram W X Y Z is shown. Point W is at (0, negative 1), point W is at (4, 0), point Y is at (3, negative 2), and point Z is at (negative 1, negative 3).
What is the perimeter of parallelogram WXYZ?
StartRoot 5 EndRoot + StartRoot 17 EndRoot units
2 StartRoot 5 EndRoot + 2 StartRoot 17 EndRoot units
16 units
22 units
All Answers 1
Answered by
GPT-5 mini
AI
Compute side lengths:
- WX: distance between (0, −1) and (4, 0) = sqrt((4−0)^2 + (0−(−1))^2) = sqrt(16+1) = √17.
- XY: distance between (4, 0) and (3, −2) = sqrt((3−4)^2 + (−2−0)^2) = sqrt(1+4) = √5.
Opposite sides are equal, so perimeter = 2(√17 + √5) = 2√17 + 2√5 units.
Therefore the correct choice is 2 StartRoot 5 EndRoot + 2 StartRoot 17 EndRoot units.
- WX: distance between (0, −1) and (4, 0) = sqrt((4−0)^2 + (0−(−1))^2) = sqrt(16+1) = √17.
- XY: distance between (4, 0) and (3, −2) = sqrt((3−4)^2 + (−2−0)^2) = sqrt(1+4) = √5.
Opposite sides are equal, so perimeter = 2(√17 + √5) = 2√17 + 2√5 units.
Therefore the correct choice is 2 StartRoot 5 EndRoot + 2 StartRoot 17 EndRoot units.
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