Ratios in the Coordinate Plane Quick Check
2 of 52 of 5 Items
Question
Use the image to answer the question.
A coordinate plane shows red paint on the X-axis and blue paint on the Y-axis. The X-axis ranges from 0 to 10 in increments of 2. The Y-axis ranges from 0 to 15 in increments of 3. The data points are left parenthesis 2 comma 3 right parenthesis, left parenthesis 4 comma 6 right parenthesis, left parenthesis 6 comma 9 right parenthesis, and left parenthesis 8 comma 12 right parenthesis.
Choose the coordinate pair to plot on the coordinate plane so the ratio stays equivalent.
(1 point)
Responses
(15, 10)
left parenthesis 15 comma 10 right parenthesis
(9, 15)
left parenthesis 9 comma 15 right parenthesis
(10, 15)
left parenthesis 10 comma 15 right parenthesis
(10, 14)
wrong @bot GPT 3.5
To ensure that the ratio stays equivalent, we need another coordinate pair that falls on the same line as the given points. This means that the ratio of the y-coordinate to the x-coordinate should be the same as the ratio of any of the given points.
Let's check the ratios of the given points:
- Ratio of (2, 3): 3/2 = 1.5
- Ratio of (4, 6): 6/4 = 1.5
- Ratio of (6, 9): 9/6 = 1.5
- Ratio of (8, 12): 12/8 = 1.5
Now, let's check the ratios of the answer choices:
- Ratio of (15, 10): 10/15 = 0.67
- Ratio of (9, 15): 15/9 = 1.67
- Ratio of (10, 15): 15/10 = 1.5
- Ratio of (10, 14): 14/10 = 1.4
The only ratio that matches the ratio of the given points is the ratio of (10, 15), so the correct answer is (10, 15).