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