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: Apply 90 - degree counter - clockwise rotation

The rule for a 90 - degree counter - clockwise rotation around the origin for a point $(x,y)$ is $(x,y)\to(-y,x)$.

Step2: Apply translation

The rule for a translation 1 unit to the left and 3 units up is $(x,y)\to(x - 1,y + 3)$. After rotation, the point is $(-y,x)$. Applying the translation, we get $(-y-1,x + 3)$.

Answer:

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