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# Point (2,3) is the vertex of a square, and point (−2,7) is the opposit

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Math Expert
Joined: 02 Sep 2009
Posts: 58402
Point (2,3) is the vertex of a square, and point (−2,7) is the opposit  [#permalink]

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17 Jan 2019, 02:59
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:22) correct 19% (00:45) wrong based on 36 sessions

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Point (2,3) is the vertex of a square, and point (−2,7) is the opposite vertex of the same square. What is the area of the square?

A 8

B 9

C 16

D 25

E 16√2

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Re: Point (2,3) is the vertex of a square, and point (−2,7) is the opposit  [#permalink]

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17 Jan 2019, 03:12
1
Bunuel wrote:
Point (2,3) is the vertex of a square, and point (−2,7) is the opposite vertex of the same square. What is the area of the square?

A 8

B 9

C 16

D 25

E 16√2

Point (2,3) is the vertex of a square, and point (−2,7) is the opposite vertex of the same square means (2,3) and (-2,7) are vertices of diagonal

Distance between (2,3) and (-2,7) =$$\sqrt{(2+2)^2+(3-7)^2}$$=$$\sqrt{2*16}$$

Area of square in terms of diagonal =$$\frac{1}{2}d^2$$

=(1/2)2*16

=16

Hence C
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Re: Point (2,3) is the vertex of a square, and point (−2,7) is the opposit  [#permalink]

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17 Jan 2019, 07:31
Bunuel wrote:
Point (2,3) is the vertex of a square, and point (−2,7) is the opposite vertex of the same square. What is the area of the square?

A 8

B 9

C 16

D 25

E 16√2

use distance formula
we get diagonal of square = 4 sqrt 2
so side = s sqrt2 = 4 sqrt2
s= 4
area = 16
IMO C
Re: Point (2,3) is the vertex of a square, and point (−2,7) is the opposit   [#permalink] 17 Jan 2019, 07:31
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