Using Ratios in the Coordinate Plane Quick Check
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Question
Use the image to answer the question.
A graph with the x-axis representing oranges ranging from 0 to 36 in increments of 3 and the y-axis representing dollars ranging from 0 to 20 in increments of 1 shows six plotted points, 3 each for option A and option B. Option A has the following points: left parenthesis 12 comma 5 right parenthesis; left parenthesis 24 comma 10 right parenthesis; and left parenthesis 36 comma 15 right parenthesis. Option B has the following points: left parenthesis 9 comma 6 right parenthesis; left parenthesis 18 comma 12 right parenthesis; and left parenthesis 27 comma 18 right parenthesis.
Which coordinate pair should be plotted next for Option A to keep the ratio the same?
(1 point)
Responses
(40, 19)
left parenthesis 40 comma 19 right parenthesis
(48, 20)
left parenthesis 48 comma 20 right parenthesis
(37, 16)
left parenthesis 37 comma 16 right parenthesis
(41, 20)
To find the next coordinate pair for Option A that would keep the ratio the same, we need to look at the ratio between the x-coordinates and the y-coordinates of the previous points.
The ratio of x-coordinates for Option A is 12:24:36, which simplifies to 1:2:3.
The ratio of y-coordinates for Option A is 5:10:15, which also simplifies to 1:2:3.
For the next coordinate pair, we want the ratio of the x-coordinate to be 4 (1 more than the previous ratio) to maintain the same pattern. Therefore, the next x-coordinate should be 36 * 4 = 144.
Similarly, we want the ratio of the y-coordinate to be 4 (1 more than the previous ratio). Therefore, the next y-coordinate should be 15 * 4 = 60.
Thus, the next coordinate pair for Option A that would keep the ratio the same is (144, 60).