Combinations of Transformations
(Lesson 7-7 extension)
Do all problems on graph paper with the following guidelines:
 Set up a four-quadrant coordinate grid with a maximum of max = 10 and
min = (-10) for both the x-axis and y-axis.
 Graph each original shape and its corresponding image(s) on the same
coordinate grid.
 Set up a new coordinate grid for each problem.
 Use a straight-edge for drawing ALL lines.
1) Triangle XYZ has the vertices of X(-1, 3), Y(2,3), and Z(3, -1).
Translate the triangle left 6 spaces and down 3 spaces and label the translated triangle
X’Y’Z’.
Then reflect the triangle over the x-axis and label it X’’Y’’Z’’.
2) Polygon KLMN has vertices of K(-1, 1), L(-3, 0), M(-2, -3), and N(0, -2).
Reflect the polygon across the y-axis, label it K’L’M’N’.
Then translate the figure up 5 spaces and right 2 spaces.
Label the final polygon as K’’L’’M’’N’’.
3) Triangle ABC has vertices of A(-1, -2), B(-3, -2), and C(-2, -4).
Make a dilation of the triangle using a scale factor of 2 and labeling the new triangle
A’B’C’.
Reflect new triangle across the x-axis and label it A’’B’’C’’.
4) Triangle RST has vertices R(1, 4), S(1, 7), and T(6, 7).
Translate the triangle right 1 space and up 2 spaces and label it R’S’T’.
Reflect the new triangle across the x-axis and label it R’’S’’T’’.
5) Trapezoid BIRD has vertices B(1, 1), I(2, 4), R(6, 4), and D(7, 1).
Reflect the trapezoid across the x-axis and label it B’I’R’D’.
Then rotate the trapezoid 90o clockwise and label it B’’I’’R’’D’’.
6) Parallelogram JUNE has vertices J(2, -2), U(6, -2), N(8, -5), and E(4, -5).
Translate the parallelogram left 2 spaces and down 3 spaces and label it J’U’N’E’.
Reflect the new parallelogram across the y-axis and label it J’’U’’N’’E’’.
7) Triangle BAT has vertices of B(1, 1), A(2, 3), and T(5, 3).
Reflect the triangle over the y-axis.
Then reflect the triangle over the x-axis.
Finally, translate the figure 7 spaces up and 2 spaces to the right, then label it B’A’T’.
8) BONUS Trapezoid MATH has vertices M(-6, 0), A(-3, -3), T(-3, -6), and H(-6, -6).
Dilate the trapezoid using a scale factor of 1⁄3, and label it M’A’T’H’.
Rotate the new trapezoid 180o.
Lastly, create another dilation using a scale factor of 4, and label it M’’A’’T’’H’’.