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.

Question

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 rotate a point 180 degrees counterclockwise around the origin in the coordinate plane, you can transform the coordinates \((x, y)\) into \((-x, -y)\).

Given the coordinates of point \(A\) are \((2, 6)\):

1. Apply the transformation: \[ A'(x', y') = (-x, -y) = (-2, -6) \]

Therefore, the new coordinates of point \(A\) after the triangle is rotated 180 degrees counterclockwise are \((-2, -6)\).