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

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

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

(−2,−4)

Answer 1

To rotate point A (2, 4) 90 degrees counterclockwise around the origin, we can use the rotation formula for a point (x, y):

• The new coordinates (x', y') after a 90 degrees counterclockwise rotation are given by: \[ x' = -y \] \[ y' = x \]

Starting with point A (2, 4):

• Apply the formula: \[ x' = -4 \] \[ y' = 2 \]

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

The correct response is: (−4, 2) left parenthesis negative 4 comma 2 right parenthesis.