Question

which sequence of transformations maps polygon abcd onto polygon wxyz?
a. a rotation of polygon abcd followed by a dilation of the image with a scale factor of 2
b. a reflection of polygon abcd followed by a dilation of the image with a scale factor of 0.5
c. a reflection of polygon abcd followed by a dilation of the image with a scale factor of 2
d. a rotation of polygon abcd followed by a dilation of the image with a scale factor of 0.5

Explanation:

1. First, analyze the orientation and size change: The smaller polygon ABCD and larger WXYZ have a similar shape, suggesting a dilation. The size of WXYZ is larger, so scale factor >1. Also, the orientation change (mirror-like) suggests a reflection first, then dilation.
2. Check scale factor: The coordinates (e.g., D(1,8), C(5,8); Y(8,8), Z(18,8) – length DC is 4, YZ is 10? Wait, better: ABCD has side lengths, WXYZ is double? Wait, ABCD: D(1,8), A(3,11), B(5,12), C(5,8). WXYZ: Y(8,8), X(8,16), W(14,14), Z(18,8). So from ABCD to WXYZ, after reflection (to flip horizontally/vertically? Wait, ABCD is left, WXYZ is right, maybe reflection over y-axis? Then dilation. The length from D to C is 4 units (x from 1 to 5), Y to Z is 10? No, wait Y is (8,8), Z is (18,8), so length YZ is 10? Wait no, ABCD: D(1,8), C(5,8) → length DC = 4. WXYZ: Y(8,8), Z(18,8) → length YZ = 10? No, maybe my coordinate reading is wrong. Wait grid: each square is 1 unit. D is at (1,8)? Wait x-axis: 0,2,4,6,8... So D is at (1,8)? No, x=1? Wait the grid lines: x=0,1,2,... So D is (1,8), C is (5,8) (x=5, y=8). Y is (8,8), Z is (18,8)? No, Z is at x=18? Wait the grid goes to 20, so Z is (18,8). So DC length: 5 - 1 = 4. YZ length: 18 - 8 = 10? No, that can't be. Wait maybe D is (1,8), C is (5,8) (x from 1 to 5, 4 units). Y is (8,8), Z is (18,8)? No, maybe Y is (8,8), Z is (18,8) → 10 units? No, maybe I messed up. Wait ABCD: D(1,8), A(3,11), B(5,12), C(5,8). WXYZ: Y(8,8), X(8,16), W(14,14), Z(18,8). So the height from Y to X is 8 units (y=8 to 16), ABCD height from D to A/B is 4 units (y=8 to 12). So scale factor 2. And the reflection: ABCD is on the left, WXYZ on the right, maybe reflection over x=6 or y-axis? So reflection first, then dilation by 2. So option C: reflection then dilation scale factor 2.

Answer:

C. a reflection of polygon ABCD followed by a dilation of the image with a scale factor of 2