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, what are the new coordinates of the point after the triangle is rotated 180 degrees counterclockwise?

Answer 1

To find the new coordinates of point \( A(2, 6) \) after the triangle is rotated 180 degrees counterclockwise about the origin, we can use the rule for rotation:

When a point \((x, y)\) is rotated 180 degrees around the origin, the new coordinates \((x', y')\) become:
\[
(x', y') = (-x, -y)
\]

For point \( A(2, 6) \):
- The x-coordinate is \( 2 \).
- The y-coordinate is \( 6 \).

Applying the rotation rule:
\[
x' = -2, \quad y' = -6
\]

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