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?

Answer 1

To find the new coordinates of point A(2, 6) after a 90-degree clockwise rotation around the origin (0, 0), you can use the following transformation rule:

For a clockwise rotation of 90 degrees: \[ (x, y) \rightarrow (y, -x) \]

Given the original coordinates of point A: \[ A(2, 6) \]

Applying the transformation:

1. The x-coordinate (2) becomes the y-coordinate (6).
2. The y-coordinate (6) becomes the negative of the x-coordinate (-2).

Thus, the new coordinates after the rotation are: \[ A'(6, -2) \]

So, after a 90-degree clockwise rotation, the new point on the triangle would be A'(6, -2).