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 6 right parenthesis, B left parenthesis 6 comma 4 right parenthesis, and C left parenthesis 2 comma 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 counterclockwise?

Answer 1

To determine the new coordinates of point A(2, 6) after a rotation of 90 degrees counterclockwise around the origin, we can use the transformation rule for rotation.

The transformation for a point \((x, y)\) after a 90-degree counterclockwise rotation about the origin is given by the formula:

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

Applying this to point A(2, 6):

1. Original point: \( A(2, 6) \)
2. After transformation:
- \( x' = -y = -6 \)
- \( y' = x = 2 \)

Thus, the new coordinates of point A after a 90-degree counterclockwise rotation are:

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

So the new point on the triangle for A after the rotation is A'(-6, 2).