The set of reflections would carry trapezoid ABCD onto itself is y = x, x axis, y = x, y axis
What set of reflections would carry trapezoid ABCD onto itself?
From the question, we have the following parameters that can be used in our computation:
The trapezoid
Where, we have
A = (-5, 1), B = (-4, 3), C = (2, 3) and D = (-1, 1)
The set of reflections would carry trapezoid ABCD onto itself is
y = x, x axis, y = x, y axis
This is so because of the following rules:
- Reflection across y = x gives (y, x)
- Reflection across the x-axis gives (y, -x)
- Reflection across y = x gives (-x, y)
- Reflection across the y-axis gives (x, y)
Using the above as a guide, we have the following:
Original: A = (-5, 1), B = (-4, 3), C = (2, 3) and D = (-1, 1)
y = x: A' = (1, -5), B' = (3, -4), C' = (3, 2) and D' = (1, -1)
x-axis: A'' = (1, 5), B'' = (3, 4), C'' = (3, -2) and D'' = (1, 1)
y = x: A''' = (5, 1), B''' = (4, 3), C''' = (-2, 3) and D''' = (1, 1)
y-axis: A'''' = (-5, 1), B'''' = (-4, 3), C'''' = (2, 3) and D'''' = (-1, 1)
Hence, the set of reflections would carry trapezoid ABCD onto itself is y = x, x axis, y = x, y axis
Question
What set of reflections would carry trapezoid ABCD onto itself?