Question

point (x, y) is reflected over the y - axis, and then translated 5 units to the right and 2 units down. write the generalized coordinates of the image.

Explanation:

Step1: Reflection over y - axis

When a point $(x,y)$ is reflected over the $y$-axis, the $x$-coordinate changes sign. So the point becomes $(-x,y)$.

Step2: Translation 5 units right

To translate a point 5 units to the right, we add 5 to the $x$-coordinate. So the point $(-x,y)$ becomes $(-x + 5,y)$.

Step3: Translation 2 units down

To translate a point 2 units down, we subtract 2 from the $y$-coordinate. So the point $(-x + 5,y)$ becomes $(-x + 5,y-2)$.

Answer:

$(-x + 5,y - 2)$