There is a rectangle on a grid the coordinates are A(-2,1), B(1,1), C(1,-1) and D(-2,-1)

Question

Imagine a counterclockwise rotation of 270 degrees about the origin of the figure. choose the coordinate of A'

Answer 1

To perform a counterclockwise rotation of 270 degrees about the origin, we can utilize the formula for rotation of a point \((x, y)\):

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

Since point A has coordinates A(-2, 1), we apply the rotation formula:

1. The x-coordinate of A is -2 and the y-coordinate is 1.
2. According to the rotation formula:
   • The new x-coordinate \(x' = y = 1\)
   • The new y-coordinate \(y' = -x = -(-2) = 2\)

Thus, the new coordinates of A' after the 270-degree counterclockwise rotation are:

\[ A'(1, 2) \]

So the coordinate of A' is (1, 2).