To maintain the same ratio with point A (11, 33), we first need to derive the ratio from point A:
The ratio of the y-coordinate to the x-coordinate for point A is: \[ \frac{y}{x} = \frac{33}{11} = 3 \]
Now, we need to determine which of the coordinates in options B (11, 23), C (15, 33), or D (15, 23) keeps this ratio of 3.
Let's evaluate each option:
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Option B (11, 23): \[ \frac{23}{11} \approx 2.09 \quad (\text{not 3}) \]
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Option C (15, 33): \[ \frac{33}{15} = 2.2 \quad (\text{not 3}) \]
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Option D (15, 23): \[ \frac{23}{15} \approx 1.53 \quad (\text{not 3}) \]
None of the coordinate pairs provided keep the same ratio of 3.
To find a point that maintains the same ratio (3), we could choose any point (x, y) such that: \[ \frac{y}{x} = 3 \implies y = 3x \]
For example, (11, 33) is already given, and another valid pair can be (15, 45), where both maintain that ratio.
If you want to stay within the options B, C, and D while maintaining the closest resemblance to the initial ratio, you could note that point C has the highest y-coordinate, which is (15, 33), but it still does not maintain the original ratio.
Thus, based on the given options, none of them keep the same ratio as point A. If you're looking for a coordinate pair that maintains the ratio of (11, 33), you'll need to create a point through the formula \(y = 3x\) rather than selecting from the provided options.