Use the image to answer the question.
A quadrilateral is plotted a coordinate plane with both the axes ranging from negative 6 to 6.
Imagine a counterclockwise rotation of 270° about the origin of the figure. Choose the coordinate of A′.
(1 point)
Responses
(−1,−2)
left parenthesis negative 1 comma negative 2 right parenthesis
(2,−1)
left parenthesis 2 comma negative 1 right parenthesis
(1,1)
left parenthesis 1 comma 1 right parenthesis
(1,2)
left parenthesis 1 comma 2 right parenthesis
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Based on the image and the counterclockwise rotation of 270° about the origin, the coordinate of A' would be (-1,-2) or left parenthesis negative 1 comma negative 2 right parenthesis.
To determine the coordinate of A' after a counterclockwise rotation of 270° about the origin, we need to apply the rotation matrix:
[x'] [cos(270°) -sin(270°)] [x]
[y'] = [sin(270°) cos(270°)] [y]
In this case, the point A has coordinates (2, -1). Plugging these values into the rotation matrix, we have:
[x'] [0 -1] [2]
[y'] = [1 0] [-1]
[x'] [0 -1] [2] = [(-1)(2) -1(-1)] = [-2 + 1]
[y'] = [1 0] [-1] [1(2) + 0(-1)] = [2]
Therefore, the coordinate of A' is (-1, 2).
Answer: (−1, 2) or left parenthesis negative 1 comma 2 right parenthesis.