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On a coordinate plane, parallelogram P Q R S is shown. Point P is at (negative 2, 5), point Q is at (2, 1), point R is at (1, negative 2), and point S is at (negative 3, 2).
In the diagram, SR = 4 StartRoot 2 EndRoot and QR = StartRoot 10 EndRoot. What is the perimeter of parallelogram PQRS?
StartRoot 10 EndRoot units
8 StartRoot 2 EndRoot + 2 StartRoot 10 EndRoot units
16 StartRoot 2 EndRoot units
8 StartRoot 2 EndRoot + 8 units
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GPT-5 mini
AI
Compute side lengths from coordinates.
PQ = distance between P(-2,5) and Q(2,1):
PQ = sqrt((2-(-2))^2 + (1-5)^2) = sqrt(4^2 + (-4)^2) = sqrt(32) = 4√2.
QR = distance between Q(2,1) and R(1,-2):
QR = sqrt((1-2)^2 + (-2-1)^2) = sqrt(1 + 9) = √10.
Perimeter of parallelogram = 2(PQ + QR) = 2(4√2 + √10) = 8√2 + 2√10 units.
So the correct choice is: 8√2 + 2√10 units.
PQ = distance between P(-2,5) and Q(2,1):
PQ = sqrt((2-(-2))^2 + (1-5)^2) = sqrt(4^2 + (-4)^2) = sqrt(32) = 4√2.
QR = distance between Q(2,1) and R(1,-2):
QR = sqrt((1-2)^2 + (-2-1)^2) = sqrt(1 + 9) = √10.
Perimeter of parallelogram = 2(PQ + QR) = 2(4√2 + √10) = 8√2 + 2√10 units.
So the correct choice is: 8√2 + 2√10 units.
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