Unit 6 · Core unit
Moving figures without changing them, and the one transformation that does change size. Order matters, which is the main source of error.
What a strong answer looks like
A strong answer applies transformations in the stated order and states which properties were preserved.
Know
Translations, reflections, and rotations preserve distance and angle, so the image is congruent to the original.
Apply
Apply each to a single point using its coordinate rule before transforming a whole figure.
Watch out
Reflecting across the wrong line, particularly confusing the diagonal with the axes.
Study move
Apply a reflection across the diagonal to three points and describe the effect.
Know
A dilation scales distances by a fixed factor about a centre, preserving angles but not lengths, so the image is similar rather than congruent.
Apply
Multiply the displacement from the centre by the scale factor.
Watch out
Scaling from the origin when the centre is elsewhere.
Study move
Dilate a figure about a non-origin centre and confirm angles are unchanged.
Know
Applying transformations in sequence generally gives a different result when the order is reversed.
Apply
Apply one transformation at a time, recording the intermediate image.
Watch out
Combining two transformations mentally and skipping the intermediate step.
Study move
Apply a reflection then a rotation, then reverse the order and compare.
Modeling drill
Reflect a point across the diagonal, rotate it a quarter turn, then translate it, recording every intermediate image.
