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If a square is formed by joining the points A(-2, 1), B(1, 5), C(5, 2) 12 Jan 2021, 09:13
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D
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Difficulty:

25% (medium)

Question Stats:

80% (01:41) correct 20% (02:28) wrong based on 79 sessions

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If a square is formed by joining the points A(-2, 1), B(1, 5), C(5, 2), and D(2, -2), what is the area of square ABCD?

A. 9
B. 16
C. 20
D. 25
E. 36
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D
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If a square is formed by joining the points A(-2, 1), B(1, 5), C(5, 2) 12 Jan 2021, 09:48
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Diagonal of the Square ABCD = AC = BD = d^2 = 7^2 + 1^2 = 50
Area of square = d^2/2 = 50/2 = 25

D is correct
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If a square is formed by joining the points A(-2, 1), B(1, 5), C(5, 2) Updated on: 12 Jan 2021, 11:12
Originally posted by LipiSinha on 12 Jan 2021, 10:47.
Last edited by LipiSinha on 12 Jan 2021, 11:12, edited 1 time in total.
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Distance between two points can be calculated by the formula sq rt [(x1-x2)^2 + (y1-y2)^2].

Using any two consecutive points, the side of the square can be calculated as 5.

So, required area will be 25.

Also, since this is a square, the area can be calculated only by using (x1-x2)^2 + (y1-y2)^2.

The answer will be D.

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If a square is formed by joining the points A(-2, 1), B(1, 5), C(5, 2) 12 Jan 2021, 10:59
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Asked:If a square is formed by joining the points A(-2, 1), B(1, 5), C(5, 2), and D(2, -2), what is the area of square ABCD?

Let the side of the square be x.

x^2 = (-2-1)^2 + (1-5)^2 = 9+16 = 25

Area of the square = side^2 = x^2 = 25

IMO D

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If a square is formed by joining the points A(-2, 1), B(1, 5), C(5, 2) 12 Jan 2021, 13:13
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D=25

Posting an alternative approach that I found more intuitive. I plotted the points listed above, then I connected the points to create the square. After I created the square, I drew triangles with equal areas (A=6) to create a larger square. The sides of the larger square aligned with the coordinate plane better and I was able to determine that the side of the large square =7.

I then subtracted area of the large squares from the sum of the areas of the smaller triangles --> (7^2) - (6+6+6+6) = 25.
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If a square is formed by joining the points A(-2, 1), B(1, 5), C(5, 2) 28 Oct 2025, 07:48
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