How would you describe this series of transformations?
Translation of (2,0) and then reflection across the x-axis 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.
Reflection across the y-axis and then a translation of (−3,−5) shows that triangle ABC is congruent to triangle A′′B"C".
Rotation of 90 degrees clockwise and then reflection across the x-axis shows that triangle ABC is congruent to triangle A′′B"C".
The series of transformations described consists of a translation, a reflection, and a rotation.
In the first transformation, triangle ABC is translated by 2 units to the right and 0 units up, resulting in triangle A''B"C".
In the second transformation, the translated triangle A''B"C" is reflected across the x-axis, changing its orientation but preserving its shape. This reflection shows that triangle ABC is congruent to triangle A''B"C" since they have the same size and shape but different orientations.
In the third transformation, the reflected triangle A''B"C" is further transformed by a reflection across the y-axis, which changes its orientation once again but maintains its congruence to triangle ABC. Following this reflection, a translation of -3 units to the left and -5 units down is applied to the triangle, resulting in the congruent triangle A''B"C".
Lastly, in the fourth transformation, the rotated triangle A''B"C" is subject to a 90-degree clockwise rotation. After this rotation, the triangle is reflected across the x-axis, further altering its orientation but preserving its congruence to triangle ABC.