Question

transformation detective
youre designing the transformation logic for a grid - based video game level. a triangle starts in its original position - triangle abc - and will move in three different ways.
your job is to apply each transformation, describe the results mathematically, and explain how you know your answers are correct. no images are given - you must visualize or sketch them yourself to complete the analysis.
question 4
3 points
which transformation(s) preserved the triangles orientation?

Explanation:

Translation preserves orientation. Rotation (if it's a rotation that doesn't flip the figure, like a \(360^{\circ}\) rotation which is equivalent to no rotation in terms of orientation, or a \(180^{\circ}\) rotation which changes orientation, but if we assume a rotation that is a multiple of \(360^{\circ}\) or a rotation that is a proper rotation without reflection - like a \(90^{\circ}\) rotation clockwise or counter - clockwise in a plane where the coordinate system is right - handed, it preserves orientation). However, reflection changes orientation. Since the problem is about a triangle moving in three different ways (assuming one is translation, one is rotation, and one is reflection), translation and rotation (non - \(180^{\circ}\) and proper rotations) preserve orientation.

Answer:

Translation and rotation (assuming non - \(180^{\circ}\) and proper rotations) preserve the triangle's orientation.