Coordinate rules to memorize. 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).
Vocabulary
dilation: A transformation that changes size but not shape, using a scale factor.
congruent: Same size and same shape; one figure maps to the other by rigid motions.
Practice (no calculator unless marked)
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′?
A. Reflection over the x-axis and then a rotation of 180° about the origin
B. Reflection over the x-axis and then a rotation of 90° about the origin
C. Reflection over the y-axis and then a rotation of 180° about the origin
D. Reflection over the y-axis and then a rotation of 90° about the origin
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?
A. Line segment EF is congruent to line segment CD.
B. Line segment EF is perpendicular to line segment CD.
C. Line segment EF is twice the length of line segment CD.
D. Line segment EF is one-half the length of line segment CD.
Trent draws a triangle with one interior angle measuring 34°. Which angle measures could be the measures of the other two interior angles in Trent’s triangle?
A. 46° and 90°
B. 53° and 127°
C. 66° and 80°
D. 68° and 68°
On a coordinate plane, triangle ABC is rotated 90° clockwise about the origin and then dilated with a scale factor of 2 centered at the origin to form triangle A′B′C′. Which statement describes the relationship between the triangles?
A. They are similar and congruent.
B. They are similar but not congruent.
C. They are congruent but not similar.
D. They are neither congruent nor similar.
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′?
A. (−4, 5)
B. (−4, 6)
C. (0, 5)
D. (6, −4)
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′?
A. Reflection over the x-axis and then a rotation of 180° about the origin
B. Reflection over the x-axis and then a rotation of 90° about the origin
C. Reflection over the y-axis and then a rotation of 180° about the origin
D. Reflection over the y-axis and then a rotation of 90° about the origin
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?
A. Line segment EF is congruent to line segment CD.
B. Line segment EF is perpendicular to line segment CD.
C. Line segment EF is twice the length of line segment CD.
D. Line segment EF is one-half the length of line segment CD.
Trent draws a triangle with one interior angle measuring 34°. Which angle measures could be the measures of the other two interior angles in Trent’s triangle?