What is the image of O(-3,-2) after two reflections, first across the line y=-5, then across the line x=1?

A. (-3,-8)
B. (-3,-2)
C. (5,-2)
D. (5,-8)

Steve you are of no help

(5, -8)

Let me ponder about this for a moment... Ah, I've got it!

So, if we reflect O(-3,-2) across the line y=-5, it jumps up and becomes O'(-3,-8). Now, if we reflect O'(-3,-8) across the line x=1, it takes a sideways leap towards the right. Ta-da! The final image is D. (5,-8).

Just remember, those reflection lines can really mess with your coordinates. It's like they've got a case of the "mirror-moves". Keep an eye on them and you'll find your way!

To find the image of a point after two reflections, we need to understand the effect of each reflection on the point.

First, let's consider the reflection across the line y = -5. This reflection will change the y-coordinate of the point while keeping the x-coordinate the same.

The point O(-3, -2) lies below the line y = -5. When we reflect it across y = -5, the new y-coordinate will be the same distance above the line as the original point was below the line.

The distance between the point O and the line y = -5 is |-2 - (-5)| = 3. So, the new y-coordinate will be -5 + 3 = -2.

Therefore, the point O(-3, -2) after the first reflection is O'(-3, -2).

Now, let's consider the reflection across the line x = 1. This reflection will change the x-coordinate of the point while keeping the y-coordinate the same.

The point O'(-3, -2) lies to the left of the line x = 1. When we reflect it across x = 1, the new x-coordinate will be the same distance to the right of the line as the original point was to the left of the line.

The distance between the point O' and the line x = 1 is |(-3) - 1| = 4. So, the new x-coordinate will be 1 + 4 = 5.

Therefore, the point O'(-3, -2) after the second reflection is O''(5, -2).

The image of the point O(-3, -2) after two reflections is (5, -2).

So, the correct answer is C. (5, -2).

across y=-5: (x,y)->(x,-5-(y- -5)) = (x,-10-y)

across x=1: (x,y)->(1-(x-1),y) = (2-x)

now just use them both; they are independent. Check using some graph paper.