How would you describe this series of transformations?
Reflection across the y-axis and then a translation of (−3,−5) shows that triangle ABC is congruent to triangle A′′B"C".
Since triangles ABC and A′′B"C" do not have the same orientation, they are not congruent.
Rotation of 90 degrees clockwise and then reflection across the x-axis shows that triangle ABC is congruent to triangle A′′B"C".
Translation of (2,0) and then reflection across the x-axis shows that triangle ABC is congruent to triangle A′′B"C".
The first series of transformations includes a reflection across the y-axis and then a translation of (-3,-5). This means that the triangle ABC is flipped across the y-axis and then moved 3 units to the left and 5 units down, resulting in triangle A''B"C". However, since both triangles do not have the same orientation, they are not congruent.
The second series of transformations involves a rotation of 90 degrees clockwise and then a reflection across the x-axis. This means that triangle ABC is rotated 90 degrees in a clockwise direction and then flipped across the x-axis, resulting in triangle A''B"C". The fact that both triangles undergo the same transformations indicates that they are congruent.
The third series of transformations consists of a translation of (2,0) and then a reflection across the x-axis. This means that triangle ABC is moved 2 units to the right and then flipped across the x-axis, resulting in triangle A''B"C". Similar to the previous example, the fact that both triangles undergo the same transformations shows that they are congruent.