Question

Triangle ABC below is reflected across the y-axis and then translated 1 unit right and 2 units down.

a) Write the coordinates of the vertices of the image after reflection.
b) Write a rule for the translation. Use arrow notation.
c) Write the coordinates of the vertices of the new image after translation.

Answer 1

Any point with coordinates (x, y) reflected across the y-axis is going to have the opposite x value that it did before.
You should be able to find the coordinates yourself for part a. (you didn't provide the original ones so I can't help you there)
Here is the "rule" for a reflection across the y-axis:

`(x,\ y)\rightarrow(-x,\ y)`
And when we go 1 unit to the right and 2 down, that's the same as

`(x,\ y)\rightarrow(x+1,\ y-2)`

Combining those into one rule is pretty simple, Use our result for the first in the second and we would get
`(-x+1,\ y-2)`, so the rule is

.
Part A is asking for the coordinates after the reflection (x, y) ⇒ (-x, y).
Part C is asking for the coordinates after the full translation ⇒ (-x+1, y-2)