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
(4,−2)
(−2,−4)
(−4, 2)
(−4,−2)
1 answer
To find the new coordinates of point A(2, 4) after rotating 90 degrees counterclockwise around the origin, we can use the following transformation:
When a point (x, y) is rotated 90 degrees counterclockwise, the new coordinates (x', y') become: \[ (x', y') = (-y, x) \]
Applying this to point A(2, 4):
Thus, after the rotation, the new coordinates for point A are (-4, 2).
The correct response is:
(−4, 2)
