Answer:
Reflected across x-axis followed by a dilation with a scale factor of 2 about the origin.
Explanation:
It's clear from the graph,
Polygon ABCDE is reflected across x-axis then dilated so that it overlaps polygon A'B'C'D'E'
Let's choose a point A having coordinates (-2, -1)
By reflecting point A across x-axis,
Rule to be followed for the reflection,
(x, y) → (x, -y)
By this rule, coordinates of the image point A will be,
A(-2, -1) → A"(-2, 1)
Now point A"(-2, 1) has been dilated by a scale factor = k to form an image points A'(-4, 2).
Rule for the dilation of a point about the origin is,
A"(x, y) → A'(kx, ky)
A"(-2, 1) → A'(-2k, k)
Since, coordinates of point A' are (-4, -2),
Therefore, -2k = -4
k = 2
k = 2
Hence, polygon ABCDE was reflected across x-axis followed by a dilation with a scale factor of 2 about the origin to form polygon A'B'C'D'E'.