bob claims that he can map rectangle 1 to rectangle 2 select all of the transformations or series of transformation that support his claim

The first thing you need to notice is that each mark in the coordinate axis represents 2 units.

Now, let's analyze each option that maps rectangle 1 to rectangle 2.

Reflection over the line x = 1, and a translation of 2 units down.

You can see that the right end of rectangle 1 us located at x = -2

The distance between x = -2 and the line of reflection is:

1 -  (-2) = 3

Then the left end of the reflected rectangle will e 3 units at the right of x = 1.

1 + 3 = 4

Will be at x = 4, same as rectangle 2.

Now we move it 2 units down, and we will have rectangle 1 mapped into rectangle 2.

Translation of 12 units right, and then 2 units down.

The right end of rectangle 1 is at x = -2

The right side of rectangle 2 is at x = 10

The difference is 10 -(-2) = 12

Then we must move rectangle 1 12 units to the right.

Now, same as before, we can move rectangle 1 2 units down and we will have rectangle 1 mapped into rectangle 2.

Rotation of 180° around the point (1, 4)

This means a reflection over the line x = 1, followed of a reflection over the line y = 4.

We already see that a reflection over the line x = 1 leaves rectangle 1 right above rectangle 2. And the line that separates them is the line y = 4, then when we do a reflection over that line, we will have rectangle 1 mapped into rectangle 2.

1. d.90

2. e. none of these (80)

3. a. 0

4. b. 6

5. e. none of these (10)

6. a. 5

its a straight line parallel to the time axis