Final answer:
a. One transformation that maps triangle ABC to triangle PQR is a translation. b. Two reflections that map triangle ABC to triangle PQR are a reflection over the x-axis and a reflection over the y-axis. c. To reflect triangle ABC across the line y = x, you need to swap the x-coordinates and y-coordinates of each vertex.
Step-by-step explanation:
a. One transformation that maps triangle ABC to triangle PQR is a translation. To perform a translation, you shift the vertices of the triangle horizontally and/or vertically by a certain amount. For example, if you shift triangle ABC 2 units to the right and 3 units up, you will have triangle PQR.
b. Two reflections that map triangle ABC to triangle PQR are a reflection over the x-axis and a reflection over the y-axis. A reflection over the x-axis will change the sign of the y-coordinates of the vertices of triangle ABC, resulting in triangle A'B'C'. Then, a reflection over the y-axis will change the sign of the x-coordinates of the vertices of triangle A'B'C', resulting in triangle PQR.
c. To reflect triangle ABC across the line y = x, you need to swap the x-coordinates and y-coordinates of each vertex. For example, if the coordinates of triangle ABC are A(2, 4), B(5, 7), and C(3, 6), after reflecting across the line y = x, the coordinates of triangle PQR will be P(4, 2), Q(7, 5), and R(6, 3).