Question

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) left parenthesis 4 comma negative 2 right parenthesis(−2,−4)left parenthesis negative 2 comma negative 4 right parenthesis(−4,−2) left parenthesis negative 4 comma negative 2 right parenthesis(−4, 2)

Answer 1

To find the new coordinates of point A (2, 4) after rotating the triangle 90 degrees counterclockwise around the origin, you can use the following transformation formula:

If (x, y) is the original point, then after a 90-degree counterclockwise rotation, the new coordinates (x', y') will be:
\[
(x', y') = (-y, x)
\]

For point A (2, 4):
- x = 2
- y = 4

After applying the transformation:
\[
x' = -y = -4
\]
\[
y' = x = 2
\]

Thus, the new coordinates for point A after the rotation are (-4, 2).

Therefore, the answer is \((-4, 2)\).