A quadrilateral is plotted on a coordinate plane with both the axes ranging from negative 10 to 10.
Imagine a 90° (counterclockwise) rotation about the origin of the figure in the image. Select the coordinate of D′.
(1 point)
Responses
(4,−8)
left parenthesis 4 comma negative 8 right parenthesis
(−8,4)
left parenthesis negative 8 comma 4 right parenthesis
(8,−4)
left parenthesis 8 comma negative 4 right parenthesis
(8,4)
left parenthesis 8 comma 4 right parenthesis
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In a 90° counterclockwise rotation about the origin, the x-coordinate of a point becomes its y-coordinate, and the y-coordinate becomes the negative of its x-coordinate.
Looking at the given options, we need to find the point D' after the rotation. In the original figure, D is at (4, -8). After the rotation, the x-coordinate of D' will be -8, and the y-coordinate will be the negative of 4.
Therefore, the coordinate of D' is (-8, -4), which is option (B) left parenthesis negative 8 comma 4 right parenthesis.
To find the coordinate of D' after a 90° counterclockwise rotation about the origin, you will need to swap the x and y coordinates of D and negate the new x coordinate.
From the given coordinates (4, -8) of point D, we will swap the x and y coordinates to get (-8, 4).
Therefore, the coordinate of D' after the rotation would be (−8, 4).