Unit 7 · Transformations, Congruence & Similarity
Rigid motions (translations, rotations, reflections) produce congruent figures. Dilations produce similar figures.
Translate (x, y) → (x + a, y + b). Reflect over x-axis: (x, −y). Over y-axis: (−x, y). Rotate 90° counterclockwise about the origin: (−y, x). Dilate from origin by k: (kx, ky).
A transformation that changes size but not shape, using a scale factor.
Example: A dilation of 3 from the origin sends (2, 1) to (6, 3).
Same size and same shape; one figure maps to the other by rigid motions.
Example: A triangle and its rotation are congruent.
Try the prompt first. The steps stay folded until you ask to see them.
Triangle ABC has A(2, 1). Translate 3 left and 2 up, then reflect over the y-axis. Where is A''?
Watch for
Rotating 90° as (y, x) instead of (−y, x)
90° CCW about the origin swaps and changes the first sign.
Fix: Test with (1, 0): it should land on (0, 1).
Submit each answer to check it. The key is not shown until you do.
Trapezoid ABCD and its image A′B′C′D′ are shown on the coordinate plane. Which series of transformations could be applied to map trapezoid ABCD onto trapezoid A′B′C′D′?
Line segment CD is graphed on a coordinate plane. The line segment is reflected over the y-axis and then rotated 90° clockwise about the origin to create line segment EF. Which statement is always true about line segment EF?
Quadrilateral ABCD is graphed on a coordinate plane. Vertex A is located at (−2, 3). The quadrilateral is dilated by a scale factor of 2, with the center of dilation at the origin, to form quadrilateral A′B′C′D′. Which ordered pair represents the location of vertex A′?
Trace the pre-image on graph paper and physically slide/flip it.
Connect to Algebra I: f(x) + k is a vertical translation of a function graph.
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