Question

How do I solve this problem?

What is the image of O(2,5) after two reflections, first across the line y=5, and then across the line x=-3

Answer 1

a) Swap the x- and y-coordinates.

P=(-7, -4) ==> P'=(-4, -7)
Q=(-7, -8) ==> Q'=(-8, -7)
R=(3, -3) ==> R'=(-3, 3)

3rd selection is correct.


b) Negate the y-coordinates.

P=(-3, 8) ==> P'=(-3, -8)
Q=(-6, -4) ==> Q'=(-6, 4)
R=(1, 1) ==> R'=(1, -1)

None of the possible selections is correct. [I suspect Q'(-6,-4) is a misprint in the 3rd option.]


c) Negate the x-coordinates

P=(-2, -4) ==> P'=(2, -4)
Q=(2, -5) ==>Q'=(-2, -5)
R=(-1, -8) ==> R'=(1, -8)

3rd selection is correct.


d) You left out the 2nd line equation in the question; but I can at least help you with the first reflection across y = -5.

y = -5 is a vertical line, so you're going to be changing the x-coordinate of the point. Figure out the difference between x and -5, and then subtract that difference from -5.

x' = -5 - (x - -5) = -5 - (x + 5) = -5 - x - 5 = -10 - x

So for O=(-2, -1)...

x' = -10 - (-2) = -10 + 2 = -8

After the first reflection, O'=(-8, -1).

Answer 2

do you understand this?

Answer 3

not really, i am trying to though