Question

question
determine a series of transformations that would map polygon abcde onto polygon abcde?
a followed by a .
try

Explanation:

First, identify the size change: the original polygon ABCDE is smaller than A'B'C'D'E', so it is enlarged (dilated) by a scale factor. Comparing corresponding side lengths (e.g., AE is 2 units, A'E' is 6 units, so scale factor is $\frac{6}{2}=3$) from the origin (or center of dilation at (0,0)). Then, identify the position shift: after dilation, the dilated figure needs to be moved up and right. The original point A(1,0) dilated by 3 is (3,0); to reach A'(2,3), we shift left 1 and up 3? No, correct: original A(1,0), final A'(2,3). First, dilate ABCDE by a scale factor of 3 with the origin as the center of dilation: (x,y)→(3x,3y). So A(1,0)→(3,0), B(4,0)→(12,0), C(4,-2)→(12,-6), D(3,-3)→(9,-9), E(1,-3)→(3,-9). Then translate this dilated figure left 1 unit and up 12 units: (x,y)→(x-1, y+12). (3-1, 0+12)=(2,12)? No, A' is (2,3). Correct approach: first translate, then dilate? No, observe the orientation is same, so first dilation, then translation. Original A(1,0) to A'(2,3): the scale factor is 3, so reverse: A'(2,3) scaled down by 1/3 is ($\frac{2}{3}$,1), which is not A. So first translate ABCDE up 3 units and right 1 unit: (x,y)→(x+1, y+3), A(1,0)→(2,3) which matches A', but then size is wrong. So correct: first dilation by scale factor 3, then translation. Wait, original AE length is 3 units (from y=0 to y=-3), A'E' is 9 units (y=3 to y=12? No, A'(2,3) to E'(12,3) is 10 units? No, A(1,0) to E(1,-3) is 3 units, A'(2,3) to E'(12,3) is 10 units? No, count grid squares: ABCDE: AE is 2 vertical squares, A'E' is 6 vertical squares, so scale factor 3. Original A(1,0), after dilation by 3: (3,0). To get to A'(2,3), we subtract 1 from x, add 3 to y: (3-1, 0+3)=(2,3). So the transformations are:

1. Dilate polygon ABCDE by a scale factor of 3 with the origin (0,0) as the center of dilation.
2. Translate the dilated polygon 1 unit left and 3 units up.

Alternatively, the order can be translation first then dilation, but dilation after translation would use a different center. The most straightforward is dilation followed by translation.

Answer:

First: Dilation by a scale factor of 3 with the origin as the center of dilation
followed by a: Translation 1 unit left and 3 units up