I appreciate any help you can give me.

Here is my question:

Find the coordinates of the images of A(2,3), and B(-2,3) under the following transformations. Assume that all size transformations are centered at the origin.

a. A size transformation with scale factor 2 followed by a translation with a slide arrow from (2,1) to (3,4)

b. A translation with a slide arrow from (2,1) to (3,4) followed by a size transformation with scale factor 2

c. What can you conclude from your answers to parts (a) and (b) concerning the order in which the transformations are performed?

To find the coordinates of the images of point A(2,3) and point B(-2,3) under the given transformations, we will follow these steps for each transformation and combine the results at the end:

a. Size transformation with scale factor 2 followed by a translation with a slide arrow from (2,1) to (3,4):
1. Apply the size transformation to each point by multiplying their coordinates by the scale factor:
For point A: (2 * 2, 3 * 2) = (4, 6)
For point B: (-2 * 2, 3 * 2) = (-4, 6)

2. Apply the translation to each point by adding the slide arrow coordinates to their corresponding coordinates:
For point A: (4 + 3, 6 + 4) = (7, 10)
For point B: (-4 + 3, 6 + 4) = (-1, 10)

b. Translation with slide arrow from (2,1) to (3,4) followed by a size transformation with scale factor 2:
1. Apply the translation to each point by subtracting the slide arrow coordinates from their corresponding coordinates:
For point A: (2 - 2, 3 - 1) = (0, 2)
For point B: (-2 - 2, 3 - 1) = (-4, 2)

2. Apply the size transformation to each point by multiplying their coordinates by the scale factor:
For point A: (0 * 2, 2 * 2) = (0, 4)
For point B: (-4 * 2, 2 * 2) = (-8, 4)

c. Based on the results of parts (a) and (b), we can conclude that the order of transformations matters. The images obtained in part (a) are different from those in part (b), indicating that the order in which transformations are performed affects the final result.

In summary, the coordinates of the images are as follows:
a. The image of A(2,3) under the given transformations is (7,10), and the image of B(-2,3) is (-1,10).
b. The image of A(2,3) under the given transformations is (0,4), and the image of B(-2,3) is (-8,4).

Remember to always apply transformations in the given order to get accurate results.