Which sequences of transformations map IJKL onto I’J’K’L’? Select all that apply.

To determine which sequences of transformations map IJKL onto I’J’K’L’, we need to evaluate each option.

1. A rotation 90° counterclockwise around the origin followed by a reflection across the line x = -1.

– A rotation of 90° counterclockwise changes the coordinates (x, y) to (-y, x). This would then be reflected across x = -1. Depending on the positions of points I, J, K, and L, this might or might not match I’J’K’L’.

2. A translation down 2 units followed by a reflection across the line y = x.

– Translating down 2 units moves each point 2 units lower on the y-axis, and reflecting across y = x swaps the x and y coordinates. This often changes the orientation and position of points, possibly leading to I’J’K’L’ depending on their original position.

3. A rotation 180° around the origin followed by a reflection across the line x = 2.

– A rotation of 180° around the origin changes (x, y) to (-x, -y). A reflection across x = 2 would not usually align IJKL with I’J’K’L’ strictly.

4. A reflection across the line y = x followed by a translation left 2 units.

– Reflecting across y = x swaps coordinates,