Geometry reflections

[rachelmaddie]

Find the endpoints of the image of AB.
Reflect AB over the x-axis and rotate 90 degrees counterclockwise about the origin.

A” (-3, 1) B” (-5, 3)
A” (-3, -5) B” (-1, -3)
A” (3, -5) B” (1, -3)
A” (-3, 5) B” (-1, 3)

 

[rachelmaddie]

It says to multiply the y-coordinate of each point by –1. Then change each point (x, y) to (–y, x) to perform the rotation.
Here is my work:
The original points are A(-5, 3), B(-3, 1)
Multiply the y-coordinate of each point by -1
3 • (-1) = -3
1 • (-1) = -1
A(-5, -3), B(-3, -1)
A”(-3, -5), B”(-1, -3)

Is this correct?

 

[rachelmaddie]

Correction:
A’(-5, -3), B’(-3, -1)
Multiply the y coordinate of each point by -1
-3 • -1 = 3
-1 • -1 = 1
A’(-5, 3) changes to A”(3, -5)
B’(-3, 1) changes to B”(1, -3)
So, the best option is C

 

[Otis]

A’(-5, -3), B’(-3, -1) …
A’(-5, 3) … B’(-3, 1) …

Hi rachel. The coordinates above are correct, but your notation is not. (Don't use the same label for different points.)

If you treat the two steps provided for the rotation as two separate transformations, then use symbols A, A', A'' and A''' with your steps. Otherwise, treat the rotation as a single transformation and skip reporting the intermediate step above. (Use your scratch paper, instead.)

And, yes, the answer is the third choice listed in your op.

?

 

[rachelmaddie]

Hi rachel. The coordinates above are correct, but your notation is not. (Don't use the same label for different points.)

If you treat the two steps provided for the rotation as two separate transformations, then use symbols A, A', A'' and A''' with your steps. Otherwise, treat the rotation as a single transformation and skip reporting the intermediate step above. (Use your scratch paper, instead.)

And, yes, the answer is the third choice listed in your op.

?

Can you show me?

 

[pka]

Find the endpoints of the image of AB.
Reflect AB over the x-axis and rotate 90 degrees counterclockwise about the origin.
A” (-3, 1) B” (-5, 3)
A” (-3, -5) B” (-1, -3)
A” (3, -5) B” (1, -3)
A” (-3, 5) B” (-1, 3)

The reflection over the \(\displaystyle x-\)axis.
\(\displaystyle \mathcal{RL_x}:\left( {\begin{array}{*{20}{c}} 0&{ - 1} \\ 1&0 \end{array}} \right)\left( {\begin{array}{*{20}{c}} x \\ y \end{array}} \right) = \left( {\begin{array}{*{20}{c}} { - y} \\ x \end{array}} \right)\)

The rotation about orgin\(\displaystyle (0,0)~.\)
\(\displaystyle \mathcal{RO}_{(0,0)}:
\left( {\begin{array}{*{20}{c}} {\cos (\theta )}&{ - \sin (\theta )} \\ {\sin (\theta )}&{\cos (\theta )} \end{array}} \right)\left( {\begin{array}{*{20}{c}} x \\ y \end{array}} \right)\)

So do the composition.

 

[Otis]

Can you show me?

You've posted the correct answer; I had commented on a mistake in your labeling.

What is it that you would like me to show you?

\(\;\)

 

[rachelmaddie]

You've posted the correct answer; I had commented on a mistake in your labeling.

What is it that you would like me to show you?

\(\;\)

I wanted you to show me how to do the notation the proper way.

 

[Otis]

… show me how to do the notation …

Hi. I explained the issue and notation in post #4. What parts are unclear?

If you start with some point A, and you do two transformations, then you write them as A' and A''.

If you do three transformations, then you write them as A', A'' and A'''.

\(\;\)

 

[rachelmaddie]

Hi. I explained the issue and notation in post #4. What parts are unclear?

If you start with some point A, and you do two transformations, then you write them as A' and A''.

If you do three transformations, then you write them as A', A'' and A'''.

\(\;\)

I’m sorry thank you!