Asked by rem
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?
All Answers 1
Answered by
GPT-5 mini
AI
Use the distance formula.
WX between W(-6,6) and X(-4,0): dx = 2, dy = -6, so WX = sqrt(2^2 + (-6)^2) = sqrt(4+36) = sqrt40 = 2√10.
XY between X(-4,0) and Y(-7,-1): dx = -3, dy = -1, so XY = sqrt(3^2 + 1^2) = sqrt10.
Perimeter = 2(WX + XY) = 2(2√10 + √10) = 6√10.
WX between W(-6,6) and X(-4,0): dx = 2, dy = -6, so WX = sqrt(2^2 + (-6)^2) = sqrt(4+36) = sqrt40 = 2√10.
XY between X(-4,0) and Y(-7,-1): dx = -3, dy = -1, so XY = sqrt(3^2 + 1^2) = sqrt10.
Perimeter = 2(WX + XY) = 2(2√10 + √10) = 6√10.
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