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 coordinates of point A(2, 6) after a 90-degree clockwise rotation around the origin, we can use the rotation formula.

For a point (x, y), after a 90-degree clockwise rotation, the new coordinates (x', y') are given by:

\[ (x', y') = (y, -x) \]

Applying this to point A(2, 6):

1. Original coordinates: (x, y) = (2, 6)
2. After rotation:
   • x' = y = 6
   • y' = -x = -2

Therefore, the new coordinates after a 90-degree clockwise rotation will be (6, -2).

So the answer is (6, -2).