The first step is to write the coordinate of corresponding vertices in triangles ABC and DEF. Let us consider vertex C in triangle ABC and the corresponding vertex F in triangle DEF. The coordinates are
C = (3, 2)
F = (- 1, - 2)
We want to transform (3, 2) to (- 1, - 2)
Recall, if we reflect a vertex, (x, y) over the x axis, the x coordinate remains the same while the sign of the y coordinate is reversed. Thus, by reflecting (3, 2) over the x axis, the new coordinate is (3, - 2)
Also, if we reflect a vertex, (x, y) over the y axis, the y coordinate remains the same while the sign of the x coordinate is reversed. Thus, by reflecting (3, - 2) over the x axis, the new coordinate is (- 3, - 2)
Recall, if a vertex, (x, y) is translated d units to the right, the new vertex would be (x + d, y). If we translate (- 3, - 2) 2 units to the right, the new vertex would be (-3 + 2, - 2) = (- 1, - 2). This corresponds to vertex F
Thus, the correct option is
A reflection in the x axis, followed by a reflection in the y axis and then a translation, 2 units to the right
Also, if we rotate a point, (x,y) 180 degrees about the origin, the new point would be (- x, - y). By rotating (3, 2) by 180 degrees about the origin, the new vertex would be (- 3, - 2). If we translate (- 3, - 2) 2 units to the right, the new point is (-3 + 2, - 2) = (- 1, - 2). This corresponds to vertex F
Thus, another correct option is
A rotation 180 degrees about the origin followed by a translation 2 units to the right
