Question

How would I find the image of (-2, -1) after two reflections, first across the line y = -5, and then across the line x = 1.

Answer 1

move the y parts up by 5, negate them, and then move them bac down by 5

same concept for the x parts

Answer 2

(-2,-1) : y = -5
+5 +5
--------------
(-2,4) : y = 0

negate the y, and move it back

(-2,-4) : y = 0
-5 -5
---------------
(-2,-9) : y=-5

Answer 3

or, consider that the reflecting axis is the midpoint such that:
\[\frac{y_1+y_2}{2}=\hat y\]
\[y_1+y_2=2\hat y\]
\[y_1=2\hat y-y_2\]

Answer 4

in this case:

y1 = 2(-5)-(-1)

y1 = -10+1 = -9

Answer 5

(4, -9)?

Answer 6

correct

Answer 7

Yay