Try starting with a rotation of 90^(∘) about the origin.
B
Practice makes perfect
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.
Starting with a rotation
Let's begin by rotating △ ABC by 90^(∘) about the origin. Performing such a transformation means the vertices of the figure change in the following way:
preimage (a,b) → image (- b,a)
Let's perform this rule on the given vertices of △ ABC.
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.
Starting with a translation
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.
