Use the image to answer the question.

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 negative 4 comma 2 right parenthesis

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

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

(−4,−2)

Answer 1

To find the new position of point A (2, 4) after a 90-degree counterclockwise rotation about the origin, we can use the following transformation rule:

1. The coordinates (x, y) after a 90-degree counterclockwise rotation become (-y, x).

Applying this to point A (2, 4):

• x = 2
• y = 4

After rotation, the new coordinates will be:

• New x = -y = -4
• New y = x = 2

Therefore, the new position of point A after the rotation is (-4, 2).

Thus, the correct response is: (−4, 2).