Question

What set of reflections and rotations would carry rectangle ABCD onto itself?

(a) Rotate 180°, reflect over the x-axis, reflect over the line y=x
(b) Reflect over the x-axis, rotate 180°, reflect over the x-axis
(c) Rotate 180°, reflect over the y-axis, reflect over the line y=x
(d) Reflect over the y-axis, reflect over the x-axis, rotate 180°

Answer 1

Carry onto itself means that the transformation ends up at the same rectangle.

Answer 2

Pick a vertex and execute the transformations.

Answer 3

im still confused.

Answer 4

Let's take the vertex (-1,1) a point on that rectangle.

Answer 5

what do i do after i take that point ?

Answer 6

if we rotate it 180 degrees we get (1,-1)

Answer 7

So i would rotate all the other points also ?

Answer 8

yes

Answer 9

There is no typo, i copied and paste it straight from the worksheet.

Answer 10

it says x axis twice

Answer 11

Can we look at part d)
What happens when you do the transformations to the point (-1,1)

Answer 12

Start with (-1,1)
Reflect over the y-axis --->(1,1)
reflect over the x-axis--->(1,-1)
rotate 180°---->(-1,1)

Answer 13

Notice that you end up at the same point you started with