Series: transformations of shape, size, orientation, and position
What this domain tests
Here the frames are linked by explicit geometric transformations rather than by counting. You must name the transformation, fix its parameter (angle, direction, axis, factor), and apply it to the next frame. Rules are frequently compound: rotate and shrink, or reflect and translate.
The primitive transformations
- Rotation: a fixed angle about a point, clockwise or anticlockwise. Handedness is preserved.
- Reflection: a mirror across a line, vertical, horizontal or diagonal. Handedness is reversed.
- Translation: position changes, orientation and size do not.
- Scaling: uniform enlargement or reduction, sometimes only along one axis.
- Substitution: one shape replaces another by a stated correspondence, such as circle to square.
Rotation or reflection?
Pick an asymmetric feature: a notch, a dot, a longer arm, a shaded corner. Trace where it goes. Under rotation, the clockwise order of features around the shape is unchanged. Under reflection it is reversed. For a symmetric outline, internal detail is the only reliable witness.
Worked example
Frame 1: a chevron pointing up, with a dot at its lower opening. Frame 2: the chevron points right and the dot sits on its left side. Frame 3: the chevron points down and the dot sits above it. The chevron turns 90 degrees clockwise each frame and the dot stays attached to the same vertex, travelling with it. A small square on the frame border moves two positions clockwise each frame independently. The next frame therefore shows a chevron pointing left with the dot on its right side, plus the border square advanced two positions. Options that rotate the chevron but leave the dot behind, or that reverse the rotation direction, are wrong.
Traps that cost marks
- Reading direction from the page rather than from the shape, which inverts the angle.
- Assuming a 180-degree rotation when the figure is actually reflected: only an asymmetric detail separates them.
- Forgetting that scaling applies to internal spacing and to attached elements, not just to the outline.
- Ignoring a second parameter, such as the angle increasing by 45 degrees each step rather than staying fixed.
- Choosing an option that is the correct rotation of the wrong starting frame.