An illustration of a coordinate plane with four quadrants shows the x and y axes extending from negative 8 to 8 in increments of 1. A triangle A B C is plotted on the graph. The triangle A B C has its vertices marked with closed points at A left parenthesis 2 comma 4 right parenthesis, B left parenthesis 6 comma 6 right parenthesis, and C left parenthesis 6 comma 2 right parenthesis.
Given point A (2, 4)
on the triangle in Quadrant I, where is the new point if the triangle is rotated 90 degrees counterclockwise?
(1 point)
Responses
(−2,−4)
left parenthesis negative 2 comma negative 4 right parenthesis
(−4, 2)
left parenthesis negative 4 comma 2 right parenthesis
(4,−2)
left parenthesis 4 comma negative 2 right parenthesis
(−4,−2)
left parenthesis negative 4 comma negative 2 right parenthesis
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1 answer
To find the new location of point A (2, 4) after a 90-degree counterclockwise rotation around the origin, we can use the rotation formula:
For a point (x, y), after a 90-degree counterclockwise rotation, the new coordinates (x', y') are given by:
\[ x' = -y \] \[ y' = x \]
For point A (2, 4):
Calculate the new x-coordinate: \[ x' = -y = -4 \]
Calculate the new y-coordinate: \[ y' = x = 2 \]
After the rotation, point A moves to (-4, 2).
So, the final answer is: (−4, 2).
