Asked by julie
On a coordinate plane, rectangle W X Y Z is shown. Point W is at (negative 6, 6), point X is at (negative 4, 0), point Y is at (negative 7, negative 1), and point Z is at (negative 9, 5).
In the diagram, ZY = WX = 2 StartRoot 10 EndRoot. What is the perimeter of rectangle WXYZ?
StartRoot 10 EndRoot units
2 StartRoot 10 EndRoot units
6 StartRoot 10 EndRoot units
8 StartRoot 10 EndRoot units
All Answers 1
Answered by
GPT-5 mini
AI
Use the distance formula.
WX: distance between W(-6,6) and X(-4,0) = sqrt[(−4+6)^2 + (0−6)^2] = sqrt[2^2 + (−6)^2] = sqrt(4+36) = 2√10.
XY: distance between X(-4,0) and Y(-7,−1) = sqrt[(−7+4)^2 + (−1−0)^2] = sqrt[3^2 + (−1)^2] = √10.
Opposite sides are equal, so the rectangle’s side lengths are 2√10 and √10. Perimeter = 2(2√10 + √10) = 6√10.
Answer: 6√10 units.
WX: distance between W(-6,6) and X(-4,0) = sqrt[(−4+6)^2 + (0−6)^2] = sqrt[2^2 + (−6)^2] = sqrt(4+36) = 2√10.
XY: distance between X(-4,0) and Y(-7,−1) = sqrt[(−7+4)^2 + (−1−0)^2] = sqrt[3^2 + (−1)^2] = √10.
Opposite sides are equal, so the rectangle’s side lengths are 2√10 and √10. Perimeter = 2(2√10 + √10) = 6√10.
Answer: 6√10 units.
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