Question

which of the following transformations will, when applied to any polygon on the coordinate plane, produce a congruent polygon? select all that apply. dilation centered at (0, 5) with scale factor 3 followed by reflection across the line y = 4 dilation centered at (5, 5) with scale factor \\(\frac{1}{2}\\) followed by rotation 270° clockwise about (1, 3) reflection across the y-axis followed by dilation centered at the origin with scale factor \\(\frac{1}{3}\\) reflection across the line y = -x + 7 followed by translation 8 units to the left and 2 units up

Explanation:

Congruent polygons have identical shape and size, so transformations must preserve side lengths. Dilations change size (scale factor ≠1), so any sequence with dilation will not produce congruent polygons. Rigid transformations (reflection, rotation, translation) preserve size and shape.

1. First option: Includes dilation (scale factor 3) → changes size, not congruent.
2. Second option: Includes dilation (scale factor $\frac{1}{2}$) → changes size, not congruent.
3. Third option: Includes dilation (scale factor $\frac{1}{3}$) → changes size, not congruent.
4. Fourth option: Only uses reflection (rigid) and translation (rigid) → preserves size/shape, produces congruent polygon.

Answer:

reflection across the line $y = -x + 7$ followed by translation 8 units to the left and 2 units up