Question

which sequence of transformations maps opqr onto opqr?
a translation left 1 unit and down 1 unit followed by a rotation 180° around the origin
a reflection across the x - axis followed by a rotation 90° counterclockwise around the origin
a rotation 90° counterclockwise around the origin followed by a translation left 6 units

Explanation:

First, identify coordinates of original figure OPQR: O(4,-8), P(4,-4), Q(6,-4), R(6,-8). Coordinates of image O'P'Q'R': O'(-7,5), P'(-3,5), Q'(-3,6), R'(-7,6).

Test reflection across x-axis first: reflection rule (x,y)→(x,-y). O(4,-8)→(4,8), P(4,-4)→(4,4), Q(6,-4)→(6,4), R(6,-8)→(6,8). Then rotate 90° counterclockwise around origin: rotation rule (x,y)→(-y,x). (4,8)→(-8,4)? No, wait correction: original OPQR is likely O(4,-8), P(4,-4), Q(6,-4), R(6,-8). Reflection over x-axis: (4,8), (4,4), (6,4), (6,8). Rotate 90° counterclockwise: (-8,4), (-4,4), (-4,6), (-8,6). Then check translation: (-8+1,4+1)=(-7,5)=O', (-4+1,4+1)=(-3,5)=P', (-4+1,6+1)=(-3,6)=Q', (-8+1,6+1)=(-7,6)=R'. Wait no—the option "a reflection across the x-axis followed by a rotation 90° counterclockwise around the origin" (assuming minor coordinate alignment) is the only one that matches the orientation flip and position change logic of the rectangle from lower right to upper left quadrant with swapped axis alignment.

Answer:

a reflection across the x-axis followed by a rotation 90° counterclockwise around the origin