Question

Find the image of (-2, 1) obtained by

Answer 1

The y-axis runs vertically, so changing the y-coordinate moves a figure up or down. Adding a number to the y-coordinate shifts the image up, while subtracting a number shifts the figure down.

So to translate 3 units down, we just subtract 3 from the y-coordinate.

Instead of (-2, 1) it's now (-2, -2) since 1 - 3 (units) = -2

Now, another way to say "reflect across the y-axis" is to say "reflect across the line x=0" since the line created by graphing x=0 is the same as the y-axis.

An image that is a reflection across the y-axis, or across the line x=0, will have opposite x-coordinates from the pre-image but identical y-coordinates.

Therefore, the rule for reflecting an image across the y-axis can be described as (x, y) → (−x, y).

So using our translated point (-2, -2) it now becomes (2, -2).

You didn't provide an image, however, all you need to find is the translated and reflected point that lies on (2, -2).