A triangle is reflected across line L and then across line m. If the lines intersect, what kind of isometry is this composition of reflections?

translation
rotation
reflection
glide reflection*****?

After a glide reflection, the point x is mapped to the point x' (3, -2). The translation part of the glide reflection is (x, y) ---> (x + 3 + y), and the line of reflection is y = -1. What are the coordinates of the original point x?

(6, 0)
(-1, 1)
(-2, -2)
(0, 0)

#1 I'm not sure on. I can never solve questions like #2. And in #2, the "--->" is a right arrow. Thanks

The full answers are:

1. D) Reflections and Glide Reflections
2. A) Translation
3. B) Rotation
4. C) Reflection
5. D) (0,0)
But I'm in honors so it might be different ^w^ Hope it helps anyway!

for the second question it is (0,0)

it is b rotation for the first one

Sam is correct

Sam was right....

... good

... is still right!!

For question #1, to determine the kind of isometry that is a composition of two reflections, we need to consider whether the lines of reflection are parallel, intersecting, or perpendicular.

If the lines of reflection intersect, then the result is a glide reflection. Therefore, the correct answer is "glide reflection" in this case.

Moving on to question #2, we are given that the point x is mapped to x' (3, -2) after a glide reflection. We also know that the translation part of the glide reflection is (x, y) ---> (x + 3, y), and the line of reflection is y = -1.

To solve for the coordinates of the original point x, we need to reverse the process. Since the line of reflection is y = -1, the reflected point x' would have the same x-coordinate but the opposite y-coordinate. So, the x-coordinate of x' is still 3, but the y-coordinate is now positive.

Therefore, to find the original point x, we subtract 3 from the x-coordinate of x' (which is 3) and take the opposite of the y-coordinate (which is -(-2)). This gives us (0, 2).

Hence, the correct coordinates of the original point x are (0, 2).

P(2,3)—> P’ by a glide reflection with the given translation and line of reflection. What are the coordinates of P? 8. (X,y)—>(x+3,y-2);y=0

9.(x,y)—>(x-4,y+2);x=0

it was b and c