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The points (1,6) and (7,-2) are two vertices of one diagonal

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by Max@Math Revolution » Tue Oct 09, 2018 6:29 pm

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[Math Revolution GMAT math practice question]

The points (1,6) and (7,-2) are two vertices of one diagonal of a square in the xy-plane. What is the area of the square?

A. 16
B. 25
C. 32
D. 36
E. 50
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by Max@Math Revolution » Thu Oct 11, 2018 12:27 am
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The length of the diagonal of the square is √{ (7-1)^2 + (6-(-2))^2 } = √100 = 10.
The side-length of the square is 10/ √2 = 5 √2 since the side-length of a square is equal to the length of its diagonal divided by √2. Thus, the area of the square is (5 √2)^2 = 50.

Therefore, E is the answer.
Answer: E
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by Scott@TargetTestPrep » Thu Oct 18, 2018 5:20 pm
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

The points (1,6) and (7,-2) are two vertices of one diagonal of a square in the xy-plane. What is the area of the square?

A. 16
B. 25
C. 32
D. 36
E. 50
By the distance formula, the length of the diagonal of the square is:

d = √[(7 - 1)^2 + (-2 - 6)^2] = √[36 + 64] = √100 = 10.

Recall that the area of a square, given a diagonal of length d, is A = d^2/2. Thus, the area of the square is:

A = 10^2/2 = 100/2 = 50

Answer: E

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