Transformation
Transformation tests reflection, rotation, translation, and enlargement on the coordinate plane, including combined transformations. SEE questions ask for image coordinates, the transformation that maps one figure to another, or properties preserved by a transformation.
Core rules
- Reflection: across the x-axis, (x,y)→(x,−y); across the y-axis, (x,y)→(−x,y); across y=x, (x,y)→(y,x); across y=−x, (x,y)→(−y,−x).
- Translation by vector (a,b): (x,y)→(x+a,y+b).
- Rotation about the origin: 90° clockwise (x,y)→(y,−x); 90° anticlockwise (x,y)→(−y,x); 180° (x,y)→(−x,−y).
- Enlargement centre origin, scale factor k: (x,y)→(kx,ky). k>1 enlarges; 0<k<1 reduces; negative k also rotates 180°.
- Reflection and rotation preserve length and angle; translation preserves both; enlargement preserves shape and angles but multiplies lengths by k.
Worked example
Point A(3,4) is reflected in the x-axis, then rotated 90° clockwise about the origin. Reflection gives (3,−4). A 90° clockwise rotation maps (x,y) to (y,−x), so the image is (−4,−3). If the question asks for a single transformation, check whether the combined effect matches a reflection in y=−x: (x,y)→(−y,−x) would send (3,4) to (−4,−3), so it does.
Traps
- Rotating the wrong way; clockwise and anticlockwise rules are different.
- Reflecting in the wrong axis, especially y=x versus y=−x.
- Applying enlargement to only one coordinate.
- Describing an enlargement without its centre and scale factor.
- Forgetting that a negative scale factor produces an image on the opposite side of the centre.