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.

Question

amistre64 · Answer

move the y parts up by 5, negate them, and then move them bac down by 5

same concept for the x parts

amistre64 · Answer

(-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

amistre64 · Answer

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

amistre64 · Answer

in this case:

y1 = 2(-5)-(-1)

y1 = -10+1 = -9

anonymous · Answer

(4, -9)?

amistre64 · Answer

correct

anonymous · Answer

Yay