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. Four triangles are plotted on the graph. The four triangles plotted are triangle A B C, triangle A prime B prime C prime, triangle A double prime B double prime C double prime, and triangle A triple prime B triple prime C triple prime. 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. The triangle A prime B prime C prime has its vertices marked with closed points at A prime left parenthesis negative 4 comma 2 right parenthesis, B prime left parenthesis negative 6 comma 6 right parenthesis, and C prime left parenthesis negative 2 comma 6 right parenthesis. The triangle A double prime B double prime C double prime has its vertices marked with closed points at A double prime left parenthesis negative 2 comma negative 4 right parenthesis, B double prime left parenthesis negative 6 comma negative 6 right parenthesis, and C double prime left parenthesis negative 6 comma negative 2 right parenthesis. The triangle A triple prime B triple prime C triple prime has its vertices marked with closed points at A triple prime left parenthesis 4 comma negative 2 right parenthesis, B triple prime left parenthesis 6 comma negative 6 right parenthesis, and C triple prime left parenthesis 2 comma negative 6 right parenthesis.

Given point A (2, 4)
on the triangle Quadrant I, where is the new point if the triangle is rotated 270 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 find the new location of point A(2, 4) after a 270-degree counterclockwise rotation around the origin (0,0), we can use the following formula for rotation:

When a point (x, y) is rotated 270 degrees counterclockwise, the new coordinates (x', y') are given by:

• x' = y
• y' = -x

Applying this to point A(2, 4):

1. x' = y = 4
2. y' = -x = -2

Therefore, the new coordinates of point A after rotation are (4, -2).

The answer is:

(4,−2)