Question

1. point (x, y) is rotated 90° counterclockwise around the origin, and then translated 1 unit to the left and 3 units up. write the generalized coordinates of the image.
2. here are the pre - image and image coordinates of points on a graph. describe the transformation.

pre - image coordinates (0,5) (-2,1) (4,3) (6,0) (-5,-1)
image coordinates (5,0) (1,2) (3,-4) (0,-6) (-1,5)

Explanation:

Step1: Apply 90 - degree counter - clockwise rotation formula

The formula for a 90 - degree counter - clockwise rotation about the origin for a point $(x,y)$ is $(x,y)\to(-y,x)$. So the rotated point is $(-y,x)$.

Step2: Apply translation

The translation is 1 unit to the left (subtract 1 from the x - coordinate) and 3 units up (add 3 to the y - coordinate). The new x - coordinate is $-y - 1$ and the new y - coordinate is $x + 3$. So the generalized coordinates of the image are $(-y - 1,x + 3)$.

Answer:

The generalized coordinates of the image are $(-y - 1,x + 3)$