Question

The points (4, 5), (−1, 7), (−2,−2), and (6.5,−10.5) reflected in the x-axis followed by the y-axis are (−4,−5), (1,−7), (2, 2), and (−6.5, 10.5).
Reflect the points (4, 5), (−1, 7), (−2,−2), and (6.5,−10.5) in the y-axis followed by the x-axis. Do you get the same results? Explain

Answer 1

Reflecting the points in the y-axis followed by the x-axis gives the same result as x-axis followed by the y-axis

Transformation

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, reflection, translation and dilation.

If a point A(x, y) is reflected along the x axis, the new point is A'(x, -y). If a point A(x, y) is reflected along the y axis, the new point is A'(-x, y).

Given the points (4, 5), (−1, 7), (−2,−2), and (6.5,−10.5). If it is reflected along the y axis it gives (-4, 5), (1, 7), (2,−2), and (-6.5,−10.5). If it is then reflected along the x axis it gives (-4, -5), (1, -7), (2, 2), and (-6.5, 10.5).

Reflecting the points in the y-axis followed by the x-axis gives the same result as x-axis followed by the y-axis

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