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 6 right parenthesis, B left parenthesis 6 comma 4 right parenthesis, and C left parenthesis 2 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 6 comma 2 right parenthesis, B prime left parenthesis negative 4 comma 6 right parenthesis, and C prime left parenthesis negative 2 comma 2 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 6 right parenthesis, B double prime left parenthesis negative 6 comma negative 4 right parenthesis, and C double prime left parenthesis negative 2 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 6 comma negative 2 right parenthesis, B triple prime left parenthesis 4 comma negative 6 right parenthesis, and C triple prime left parenthesis 2 comma negative 2 right parenthesis.

Given point A(2, 6)
on the triangle, where would the new point on the triangle be after a rotation of 90 degrees clockwise?

(1 point)
([
],[
])

Answer 1

To find the new point after a rotation of 90 degrees clockwise, we can use the standard rule for rotating points in the coordinate plane.

For a point \( (x, y) \), a rotation of 90 degrees clockwise transforms it to \( (y, -x) \).

For point A with coordinates \( (2, 6) \):

• The new x-coordinate will be the original y-coordinate: \( 6 \)
• The new y-coordinate will be the negative of the original x-coordinate: \( -2 \)

Therefore, after rotating point A(2, 6) 90 degrees clockwise, it will be at the new coordinates \( (6, -2) \).

So the answer is:

\[ ([6], [-2]) \]