BTGmoderatorLU wrote: ↑Tue Mar 03, 2020 3:13 am
Source: Manhattan Prep
X-Ycoordinategrid.jpg
If p and q are nonzero numbers, and p is not equal to q, in which quadrant of the coordinate system does point (p, p – q) lie?
1) (p, q) lies in quadrant IV.
2) (q, -p) lies in quadrant III.
The OA is
D
Let's take each statement one by one.
1) (p, q) lies in quadrant IV.
Since the point (p, q) lies in quadrant IV, p must be positive and q must be negative. We can rewrite the coordinates as (|p|, –q|).
Thus, (p, p – q) = (|p|, (|p| –*–|q|) = (|p|, (|p|+|q|). We see that both x-coordinate and y-coordinate are positive, thus, the point (p, p – q) lies in quadrant I. Sufficient.
2) (q, –p) lies in quadrant III.
Since the point (q, –p) lies in quadrant III, q must be negative and p must be positive. We can rewrite the coordinates as (–|q|, –|p|).
(p, p – q) = (|p|, (|p| –*–|q|) = (|p|, (|p| + |q|). As with Statement 1, we see that both x-coordinate and y-coordinate are positive, thus, the point (p, p – q) lies in quadrant I. Sufficient.
The correct answer:
D
Hope this helps!
-Jay
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