The Coordinate Plane Unit Test
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Question
Use the image to answer the question.
A graph with the x-axis representing scoops of red paint ranging from 0 to 12 in increments of 1 and the y-axis representing scoops of yellow paint ranging from 0 to 30 in increments of 1 shows seven plotted points, 5 for option A and 2 option B. Option A has the following points: left parenthesis 2 comma 5 right parenthesis; left parenthesis 4 comma 10 right parenthesis; left parenthesis 6 comma 15 right parenthesis; left parenthesis 8 comma 20 right parenthesis; and left parenthesis 10 comma 25 right parenthesis. Option B has the following points: left parenthesis 5 comma 11 right parenthesis and left parenthesis 10 comma 22 right parenthesis.
Which coordinate pair should be plotted next for Option B to keep the ratio the same?
(1 point)
Responses
(15, 33)
left parenthesis 15 comma 33 right parenthesis
(11, 33)
left parenthesis 11 comma 33 right parenthesis
(15, 23)
left parenthesis 15 comma 23 right parenthesis
(11, 23)
left parenthesis 11 comma 23 right parenthesis
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To keep the ratio the same, Option B should have a coordinate pair that is double the x-coordinate and double the y-coordinate of the previous point.
The previous point for Option B is (10, 22).
Doubling the x-coordinate gives us 10 * 2 = 20.
Doubling the y-coordinate gives us 22 * 2 = 44.
Therefore, the next coordinate pair for Option B should be (20, 44).
not a answer
Apologies for the confusion. To keep the ratio the same, we need to find the common ratio between the x- and y-coordinates in Option B.
The common ratio can be found by dividing the y-coordinate by the x-coordinate of each point.
For the given points in Option B:
1. (5, 11) -> Ratio = 11/5 = 2.2
2. (10, 22) -> Ratio = 22/10 = 2.2
The common ratio for both points in Option B is 2.2.
To find the next coordinate pair for Option B, we need to find a point where the ratio of the y-coordinate to the x-coordinate is also 2.2.
Among the given options, the point that satisfies this condition is (15, 33).
So, the correct answer is:
(15, 33)
To answer this question, we need to understand the given information and use it to determine the pattern or rule that Option B follows.
The information tells us that the graph has the x-axis representing scoops of red paint ranging from 0 to 12 in increments of 1, and the y-axis representing scoops of yellow paint ranging from 0 to 30 in increments of 1.
Option A has five plotted points, specifically (2, 5), (4, 10), (6, 15), (8, 20), and (10, 25).
Option B has two plotted points, specifically (5, 11) and (10, 22).
To determine the ratio that Option B follows, we can calculate the change in y divided by the change in x for the given points. Taking the first two points, (5, 11) and (10, 22), we have:
Change in y = 22 - 11 = 11
Change in x = 10 - 5 = 5
Ratio = Change in y / Change in x = 11 / 5
Now, we can use this ratio to determine the next coordinate pair for Option B.
Since the previous x-coordinate was 10, the next x-coordinate should be 15 to keep the ratio the same.
To find the corresponding y-coordinate, we can multiply the change in x (5) by the ratio we calculated:
Change in y = Change in x * Ratio = 5 * (11 / 5) = 11
Therefore, the next coordinate pair for Option B, to keep the ratio the same, should be (15, 11).
So, the correct answer is:
(15, 11)
or
left parenthesis 15 comma 11 right parenthesis.