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In the rectangular coordinate system above, if the area of rectangular

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Joined: 02 Sep 2009
Posts: 58398
In the rectangular coordinate system above, if the area of rectangular  [#permalink]

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13 Dec 2017, 21:07
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Difficulty:

5% (low)

Question Stats:

91% (01:03) correct 9% (01:08) wrong based on 53 sessions

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In the rectangular coordinate system above, if the area of rectangular region PQRS is 35, what are the coordinates of point P?

(A) (–2, –2)
(B) (–2, 5)
(C) (–3, 5)
(D) (–4, 5)
(E) cannot be determined from the given information

Attachment:

2017-12-12_2126_002.png [ 7.4 KiB | Viewed 912 times ]

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Re: In the rectangular coordinate system above, if the area of rectangular  [#permalink]

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07 Jan 2018, 08:07
Bunuel wrote:

In the rectangular coordinate system above, if the area of rectangular region PQRS is 35, what are the coordinates of point P?

(A) (–2, –2)
(B) (–2, 5)
(C) (–3, 5)
(D) (–4, 5)
(E) cannot be determined from the given information

Attachment:
2017-12-12_2126_002.png

We can find the length of QR by applying the distance formula. Length of QR = √[(5+2)^2 + (3-3)^2] = 7. And QR is perpendicular to X-axis. (as we can see its slope is infinity. Slope = (-2-5)/(3-3) = -7/0 = infinite). Now, since PQRS is a rectangle, PQ must be perpendicular to QR (and thus parallel to X-axis), and length of PQ = Area/QR = 35/7 = 5. So point P must be 5 units away from point Q towards left, and the slope of line PQ has to be 0 (a line || to x-axis has a slope of 0).

This will happen when y-coordinate of point P is 5 only, and its x-coordinate is 5 less than that of point Q (since we are moving to the left in a straight line).
So x coordinate of point P = 3-5 = -2.
and y coordinate of point P = 5.

Thus point P = (-2,5). Hence B answer
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Joined: 23 Oct 2017
Posts: 61
Re: In the rectangular coordinate system above, if the area of rectangular  [#permalink]

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07 Jan 2018, 08:37
It is clear from the cordinates, PQ perpendicular to y axis & QR, QR perpendicular to y axis & RS.
Since area = 35 and we know one side QR=7, thus PQ=5
x co-ordinate of P = x co-ordinate of Q - 5 = 3-5 =-2

Point P will have the same y cordinate as Q
Re: In the rectangular coordinate system above, if the area of rectangular   [#permalink] 07 Jan 2018, 08:37
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