Question

the graph shows quadrilaterals abcd and abcd. which sequences of transformations map abcd onto abcd? select all that apply. a reflection across the y - axis followed by a rotation 180° around the origin a rotation 180° around the origin followed by a translation right 6 units and up 2 units a rotation 90° counterclockwise around the origin followed by a translation right 2 units and up 3 units a translation right 3 units and down 2 units followed by a rotation 90° counterclockwise around the origin

Explanation:

Step1: Analyze reflection across y - axis

A reflection across the y - axis changes the sign of the x - coordinate of each point. Let the coordinates of a point in ABCD be (x,y), after reflection across the y - axis, it becomes (-x,y).

Step2: Analyze 180° rotation around the origin

A 180° rotation around the origin changes the sign of both x and y coordinates of a point. If a point has coordinates (x,y), after 180° rotation around the origin, it becomes (-x,-y).

Step3: Check the combined transformation

If we first reflect across the y - axis (x→ - x,y→y) and then rotate 180° around the origin (-x→x,y→ - y), this sequence of transformations can map ABCD onto A'B'C'D'.

Answer:

A reflection across the y - axis followed by a rotation 180° around the origin.