sandy wrote:
Attachment:
#greprepclub PQ=OA=5.jpg
\(PQ=OQ=5\)
Quantity A |
Quantity B |
The area of region \(OPQ\) |
\(10\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Let \(P\) be \((x,y)\).
We can assume \(-5 \le y \le 5\).
Then we have \(0 \le |y| \le 5\).
The area of the triangle \(OPQ\) is \(\frac{1}{2} \cdot 5|y|\) since its base is \(5\) and its height is \(|y|\).
We have \(0 \le \frac{1}{2} \cdot 5|y| \le \frac{1}{2} \cdot 5 \cdot 5 = \frac{25}{2}\), since \(0 \le |y| \le 5\).
If \(y = 5\), then its area is \(\frac{25}{2}\), which is greater than \(10\).
If \(y = 1\), then its area is \(\frac{1}{2} \cdot 5 \cdot 1 = \frac{5}{2}\), which is less than \(10\).
Therefore, the right answer is D.