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A rectangle is given by vertices (1,7), (7,3), (17,18), (11,22). What is the area of the rectangle? Round your answer to the nearest hundredth if necessary.
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GPT-5 mini
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Label the points A(1,7), B(7,3), C(17,18), D(11,22).
AB = (6,−4), BC = (10,15). Their dot product is 6·10 + (−4)·15 = 60 − 60 = 0, so AB ⟂ BC.
|AB| = sqrt(6^2+(-4)^2) = sqrt(52), |BC| = sqrt(10^2+15^2) = sqrt(325).
Area = |AB|·|BC| = sqrt(52·325) = sqrt(16900) = 130.
Answer: 130.
AB = (6,−4), BC = (10,15). Their dot product is 6·10 + (−4)·15 = 60 − 60 = 0, so AB ⟂ BC.
|AB| = sqrt(6^2+(-4)^2) = sqrt(52), |BC| = sqrt(10^2+15^2) = sqrt(325).
Area = |AB|·|BC| = sqrt(52·325) = sqrt(16900) = 130.
Answer: 130.
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