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# Square PQRS is in a rectangular coordinate plane, and has opposite ver

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Math Expert
Joined: 02 Sep 2009
Posts: 50570
Square PQRS is in a rectangular coordinate plane, and has opposite ver  [#permalink]

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11 Dec 2017, 22:13
00:00

Difficulty:

15% (low)

Question Stats:

90% (00:48) correct 10% (00:41) wrong based on 31 sessions

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Square PQRS is in a rectangular coordinate plane, and has opposite vertices at points P (4,4) and R (–4,–4). What is the area of square PQRS?

(A) 4
(B) 8
(C) 16
(D) 32
(E) 64

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Square PQRS is in a rectangular coordinate plane, and has opposite ver  [#permalink]

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12 Dec 2017, 13:10
Since the Square PQRS has opposite vertices at points P (4,4) and R (–4,–4), the line PR will
be the length of the diagonal of the square can be found using the below given formula :

Distance between two points = $$\sqrt{(x2-x1)^2 + (y2-y1)^2}$$

*where (x1,y1) and (x2,y2) are the two points.

The length of the diagonal is $$\sqrt{(-4-4)^2 + (-4-4)^2} = \sqrt{64+64} = \sqrt{128} = 8\sqrt{2}$$

The side of the square is $$\frac{diagonal}{\sqrt{2}} = 8$$

Therefore, the area of the square is $$side^2 = 8^2 = 64$$(Option E)
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Square PQRS is in a rectangular coordinate plane, and has opposite ver  [#permalink]

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12 Dec 2017, 14:14
Bunuel wrote:
Square PQRS is in a rectangular coordinate plane, and has opposite vertices at points P (4,4) and R (–4,–4). What is the area of square PQRS?

(A) 4
(B) 8
(C) 16
(D) 32
(E) 64

The sides of a square are equal, so use just one pair of x- or y-coordinates to find the length of one side.

Distance between vertices = length of side:
Subtract x- OR y-coordinates

P's x-coordinate is 4. R's x-coordinate is -4.
4 - (-4) = 8 = length of side

Area = $$s^2 = 8^2 = 64$$

*Parallel and perpendicular sides result in vertices that
lie on the same horizontal or vertical line.

Hence the distance between two vertices of a square in the xy-plane equals one vertex's x- or y-coordinate minus the other vertex's corresponding coordinate.
Square PQRS is in a rectangular coordinate plane, and has opposite ver &nbs [#permalink] 12 Dec 2017, 14:14
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