The labeled graph showing ABCDE, A'B'C'D'E', and the line of reflection x = -2 is shown. Also, m∠ A = m∠ A'.
In the question, we are given that the polygon ABCDE is reflected across the line x = - 2.
We are asked to graph and label the image A'B'C'D'E'. Also, we are asked if m∠ A = m∠ A'.
When the polygon ABCDE is reflected across the line x = - 2, all the coordinates on it are reflected across the line x = -2.
The reflection of any point with coordinates (x, y) on reflection across the line x = a, results in a point with coordinates (-x + 2a, y).
The coordinates of the vertices of the given polygon are:
A (-4, 4), B (-3, 3), C (-3, 2), D (-5, 1), and E (-5, 3).
Reflecting these points across the line x = - 2, we get:
A (-4, 4) → A' ( -(-4) + 2(-2), 4) = A' (0, 4).
B (-3, 3) → B' ( -(-3) + 2(-2), 3) = B' (-1, 3).
C (-3, 2) → C' ( -(-3) + 2(-2), 2) = C' (-1, 2).
D ( -5, 1) → D' ( -(-5) + 2(-2), 1) = D' (1, 1).
E (-5, 3) → E' ( -(-5) + 2(-2), 3) = E' (1, 3).
Plotting ABCDE, A'B'C'D'E', and the line x = -2 has been shown on the graph.
The angles m∠ A and m∠ A' are equal since ABCDE is reflected to make A'B'C'D'E' which makes the two figures congruent. And in congruent figures, the corresponding angles are equal.
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