Question

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.

Explanation:

Step1: Find rotation rule

When a point $(x,y)$ is rotated $90^{\circ}$ counter - clockwise around the origin, the transformation rule is $(x,y)\to(-y,x)$.

Step2: Apply translation

After rotation, the point is $(-y,x)$. Translating 1 unit to the left (subtract 1 from the x - coordinate) and 3 units up (add 3 to the y - coordinate), we get $(-y - 1,x + 3)$.

Answer:

$(-y - 1,x + 3)$