13. A( -2, -5 ) => A' is a glide reflection where the translation is ( x, y ) => ( x + 7, y ), and the line of reflection is y = 2. What are the coordinates of A'?

a.) ( 5, 9 )
b.) ( 5, -5 )
c.) ( -2, 2 )
d.) ( 6, 2 )

Answer:

The coordinates of A' after a glide reflection along the line y=2 and translation with the rule: (x,y) → (x+7,y) are:

A'(5,9)

Step-by-step explanation:

We are given coordinates of point A as (-2,-5)

Now first this point is reflected along the line y=2.

Hence, the coordinates of A get changed by the rule:

(x,y) → (x,y+14)

As the point A is 7 units below the line y=2 and hence after reflection it will lie 7 units above the line so the difference in y-value is of 14 units.

Hence A(-2,-5) → (-2,9)

Now this point (-2,9) is translated to get A' using the rule:

(x,y) → (x+7,y)

Hence,

(-2,9) → (-2+7,9)

(-2,9) → (5,9)

Hence, the coordinates of A' are:

(5,9)

actually, 2+7=9

-5 is 7 units below y=2

eeee is right pogchamp

right

Well, well, well! It seems we have a little transformation problem here. Let's put on our funny glasses and solve it!

First, we need to apply the translation to point A. The translation tells us to add 7 to the x-coordinate and to leave the y-coordinate unchanged. So, if we apply this operation to A(-2, -5), we get A'(-2 + 7, -5) = A'(5, -5).

Now, for the glide reflection, we have to reflect A' across the line y = 2. You can imagine it like A' sliding down a slippery hill and then bouncing off a mirror positioned at y = 2. The mirror sees A' coming from a certain angle and reflects it accordingly.

However, A'(5, -5) is already below the line y = 2. So, when we reflect it, it will stay below the line. In other words, the y-coordinate will remain the same, and only the x-coordinate may change.

Therefore, the coordinates of A' after the glide reflection are (5, -5).

So, the correct answer is b) (5, -5).

P.S. If you need any clownish jokes or silly puns, just let me know! I'm here to entertain!

To find the coordinates of A' after the glide reflection, we need to perform two transformations: a translation and a reflection.

First, let's apply the translation. The translation is defined as (x, y) => (x + 7, y), so to translate point A(-2, -5), we add 7 to the x-coordinate and leave the y-coordinate unchanged.

After the translation, the new coordinates of A' are:
A' = (-2 + 7, -5) = (5, -5)

Next, we need to apply the reflection. The line of reflection is y = 2, which means that any point on this line will remain fixed and any other point will be reflected across the line.

To reflect A' across the line y = 2, we need to find the distance between A' and the line of reflection, and then move A' in the opposite direction by the same distance.

The distance between the y-coordinate of A' (-5) and the line of reflection (y = 2) is 5 - 2 = 3 units.

Moving A' 3 units in the opposite direction means subtracting 3 from the y-coordinate:
A' = (5, -5 - 3) = (5, -8)

Therefore, the coordinates of A' after the glide reflection are (5, -8).

Comparing this with the answer choices given:
a.) (5, 9) - Incorrect
b.) (5, -5) - Correct
c.) (-2, 2) - Incorrect
d.) (6, 2) - Incorrect

So, the correct answer is b.) (5, -5).

first to (5,-5)

then to (5, 2+5) = (5,7)
ah well :(