What is the sequence of transformations…

Maths Questions

What is the sequence of transformations that maps triangle ABC to triangle A’B’C’? Select from the drop-down menus to correctly identify each step. Step 1: Step 2: There are two triangles on the coordinate plane. Triangle ABC has vertex A at (7, -1), vertex B at (2, -3), and vertex C at (2, -1). Triangle A’B’C’ has vertex A’ at (-3, 7), vertex B’ at (-1, 2), and vertex C’ at (-3, 2).

Answer

Any one of the following transformation sequences can achieve the mapping: translating up 4 units followed by a counterclockwise rotation of 90 degrees, or a counterclockwise rotation of 90 degrees followed by translating left 4 units, or a counterclockwise rotation of 90 degrees around the center point (-2, -2). Step-by-step breakdown: The vertices ABC and A’B’C’ are ordered clockwise, indicating that any reflections used must be in pairs (thus, an even number). The line CA points east, while C’A’ points north, indicating a 90¬∞ counterclockwise rotation has occurred. Normally, such rotation might suggest a single transformation around an appropriate center, but since we seek a sequence, we can consider multiple steps. Rotating the figure 90¬∞ counterclockwise results in a position 4 units east of the final destination, leading to the sequence of 90¬∞ CCW followed by a translation left by 4 units. Conversely, rotating the final figure 90¬∞ clockwise positions it 4 units north of the starting point, translating up 4 units followed by a 90¬∞ CCW rotation is another valid sequence. Notably, a 90¬∞ CCW rotation is equivalent to a 270¬∞ clockwise rotation. We have outlined some possible transformation combinations, but since we are uncertain of your exact drop-down options, a definitive choice is challenging.

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