Practice identifying, describing, and applying geometric transformations, including rigid motions, dilations, and compositions.
Read each problem carefully. Show your work in the space provided and use precise transformation notation when possible.
Translations, reflections, rotations, dilations, and compositions on the coordinate plane
Geometry - Grade 9-12
- 1
Triangle ABC has vertices A(2, 1), B(5, 1), and C(3, 4). Translate the triangle by the vector < -3, 2 >. Give the coordinates of A', B', and C'.
- 2
Point P(-4, 7) is reflected across the x-axis. What are the coordinates of P'?
- 3
Point Q(6, -2) is reflected across the y-axis. What are the coordinates of Q'?
- 4
Point R(3, -5) is rotated 90 degrees counterclockwise about the origin. What are the coordinates of R'?
- 5
Point S(-2, 8) is rotated 180 degrees about the origin. What are the coordinates of S'?
- 6
Triangle DEF has vertices D(1, 2), E(4, 2), and F(2, 6). Dilate the triangle by a scale factor of 3 centered at the origin. Give the coordinates of D', E', and F'.
- 7
Rectangle WXYZ has vertices W(-1, 1), X(3, 1), Y(3, 4), and Z(-1, 4). Reflect the rectangle across the line y = x. Give the coordinates of W', X', Y', and Z'.
- 8
A transformation maps every point (x, y) to (x + 5, y - 1). Name the transformation and describe it in words.
- 9
A transformation maps every point (x, y) to (-x, y). Name the transformation and identify the line of reflection.
- 10
Point A(2, 3) is first translated by <4, -5> and then reflected across the y-axis. What are the final coordinates of A''?
- 11
Point B(-3, 4) is reflected across the x-axis and then rotated 90 degrees clockwise about the origin. What are the final coordinates of B''?
- 12
A triangle has side lengths 5 cm, 7 cm, and 9 cm. It is dilated by a scale factor of 0.5. What are the side lengths of the image triangle, and is the image congruent or similar to the original?
- 13
Quadrilateral JKLM is rotated 270 degrees counterclockwise about the origin. Which single rotation would produce the same result, and in what direction?
- 14
Line segment AB has endpoints A(-2, 5) and B(4, 1). It is reflected across the x-axis. Does the length of the segment change? Explain.
- 15
Triangle PQR has vertices P(0, 0), Q(6, 0), and R(2, 4). Triangle P'Q'R' has vertices P'(0, 0), Q'(3, 0), and R'(1, 2). Describe the transformation from triangle PQR to triangle P'Q'R'.