Question

Find the image of O(-2,-1) after two reflections, first across the line y=-5, then across the line x=1.
A. (-2,-1)
B. (-1,-6)
C. (4,-9)
D. (1,-5)

Answer 1

we can translate, negate, then undo the translation.

O(a,b), reflect about y = k
-k -k
------------------------
O(a,b-k) reflect about y=0, negate the y part

O(a,k-b) ... y=0, now add back the k to move it all back in place
+k +k
----------------
O(a,2k-b) is the reflection about y = k


with any luck

Answer 2

reflecting about the x is the same process, just on the x parts

Answer 3

so, O' = (2(1)-2, 2(-5)-(-1)) seems about right

Answer 4

so, O' = (2(1)-(-2), 2(-5)-(-1)) seems better, since i dropped a negative

Answer 5

I would then solve (2(1)-(-2), 2(-5)-(-1)), right?

Answer 6

of course :)

Answer 7

or you could work thru it with the steps i took to develop that formula ... either way gets to the same results

Answer 8

Thanks

Answer 9

youre welcome