Question

decide whether each transformation does or does not preserve distance.
does not preserve distance \t preserves distance
dilation centered at the origin, with scale factor 0.5 \t
reflection over the line y = x \t
rotation 90° counterclockwise about the origin \t
dilation centered at the origin with scale factor 1 \t

Explanation:

1. Dilation (scale factor 0.5): Shrinks all distances by half, so it does not preserve distance.
2. Reflection over y=x: A rigid transformation that flips points across a line without changing distances between points, so it preserves distance.
3. Rotation 90° counterclockwise: A rigid transformation that turns points around the origin without changing distances between points, so it does preserve distance (the checked box in the image is incorrect here).
4. Dilation (scale factor 1): Leaves all points unchanged, so distances remain the same, preserving distance.

Answer:

Transformation	Does Not Preserve Distance	Preserves Distance
Reflection over the line y = x	❌	✅
Rotation 90° counterclockwise about the origin	❌	✅
Dilation centered at the origin with scale factor 1	❌	✅