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Try starting with a rotation of 90^(∘) about the origin.
B
In all four options we have to perform a rotation of 90^(∘) counterclockwise about the origin. There are two kinds of options we can choose from. First, by starting with a rotation of 90^(∘). Second, by starting with a translation.
| Point | (a,b) | (- b,a) |
|---|---|---|
| A | (1,2) | (- 2,1) |
| B | (3,4) | (- 4,3) |
| C | (2,2) | (- 2,2) |
Now we can draw A'B'C'.
From the diagram, we can see that A'B'C' has the same orientation as DEF. Additionally, C' and F are corresponding vertices. Therefore, if we translate △ A'B'C' 3 units to the right and 4 units down, we can map C' to F.
The transformation we have performed does not match either of the two options where the rotation of 90^(∘) comes first.
Let's arbitrarily choose to perform the first transformation, option B. This starts with a translation of 4 units to the left and 3 units down
Using the same rule as previously stated, we can determine the coordinates of the vertices of A''B''C'' after a 90^(∘) rotation about the origin
| Point | (a,b) | (- b,a) |
|---|---|---|
| A' | (- 5,- 1) | (1,- 5) |
| B' | (- 1,1) | (- 1,- 1) |
| C' | (- 2,- 1) | (1,- 2) |
Now we can draw A''B''C''.
As we can see, option B transforms △ ABC to △ DEF.