Which of the following transformations can change the size of a shape?

In 2D geometric transformations, rigid-body transformations — translation, rotation, and reflection — preserve an object's size and shape; they only change its position or orientation. Scaling works differently: it multiplies every coordinate by a scale factor (sx along x, sy along y), so the object's dimensions actually grow or shrink.

Checking each of the four listed transformations against this rule shows which one changes size:

• Rotation turns the shape about a fixed point through some angle — orientation changes, size does not.

• Reflection produces a mirror image across a line — the mirrored shape's dimensions equal the original's, so size does not change.

• Translation shifts every point by the same displacement vector — distances between points, and hence size, stay the same.

• Scaling multiplies each coordinate by a scale factor — this is exactly what changes an object's size.

So among the four transformations, scaling is the one that changes the size of a shape.