4. Compose Transformations
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Now, let's translate Figure A' 4 units to the right.
We found that the image is Figure E. This result corresponds with answer D.
| Transformation |
|---|
| 1. Rotation 90^(∘) about the origin |
| 2. Translation 13 units right |
| 3. Translation 4 units down |
To find which figure was transformed into G, we can apply the inverse of each transformation to G.
| Transformation | Inverse |
|---|---|
| 1. Rotation 90^(∘) about the origin | 1. Rotation -90 ^(∘) about the origin |
| 2. Translation 13 units right | 2. Translation 13 units left |
| 3. Translation 4 units down | 3. Translation 4 units up |
| Transformations |
|---|
| 3. Translation 4 units up |
| 2. Translation 13 units left |
| 1. Rotation -90 ^(∘) about the origin |
We will translate Figure G 4 units up, 13 units left, and then rotate it -90^(∘), which is equal to 270^(∘), about the origin. Let's start with the translation.
Now, we will rotate FigureG 270^(∘) about the origin. Recall that to perform a rotation we need to change the x- and y-coordinates of the points of the rectangle as shown in the following table.
| Angle of Rotation | Rule |
|---|---|
| 90^(∘) | (x,y)→ (- y,x) |
| 180^(∘) | (x,y)→ (- x,- y) |
| 270 ^(∘) | (x,y)→ (y,- x) |
We want to rotate FigureG 270^(∘) around the origin. Let's change the coordinates of each vertex of the translated Figure G. ccc (x,y) & → & ( y, - x) [0.5em] (-7,-2) & → & (-2,7) [0.5em] (-4,-2) & → & (-2,4) [0.5em] (-4,-5) & → & (-5,4) [0.5em] (-6,-5) & → & (-5,6) [0.5em] (-7,-3) & → & (-3,7) Let's graph the figure after rotation!
After applying the inverse of each given transformation to Figure G we got Figure B. Therefore, Figure B can be transformed into G after the given transformations! This result corresponds with answer A.
Next, let's translate it 13 units right and 4 units down.
We found that the Figure B can be transformed into G using the given transformations.