Answer:
- translation 9 units right
- reflection over the x-axis
Explanation:
You want to know how image A in the figure is transformed to image B.
Orientation
Image A has its right angle at lower left, and the short side extending upward (clockwise) from there.
Image B has the right angle at upper left, and the short side extending downward (counterclockwise) from there.
The reversal of the orientation from clockwise to counterclockwise indicates a reflection is involved. The position of the short leg on the left side of both figures indicates it is not a left-right reflection, but is an up-down reflection.
Position
The left-side leg of ∆A is located on the line x=-6. That leg of ∆B is located on the line x = 3, which is 3-(-6) = 9 units right of its location in ∆A.
The long leg of ∆A is on the line y = 2. The same leg of ∆B is on the line y = -2, which is equally far from the x-axis. The up-down reflection is over the x-axis.
Transformation
The combination of translation 9 units to the right and reflection over the x-axis is called a "glide reflection." ∆A was transformed to ∆B by a glide reflection 9 units right and over the x-axis.
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Additional comment
Rotation will not change the clockwise/counterclockwise orientation of the figure. No rotation is involved here.
Alternatively, the figure could be reflected over the point (-1.5, 0) and then reflected again over the line containing the short leg of the triangle. Or, it could be reflected over the point (-4.5, 0) and then the y-axis.
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