Question

what set of reflections would carry trapezoid abcd onto itself? (1 point) trapezoid abcd is shown. a is at negative 5, 1. b is at negative 4, 3. c is at negative 2, 3. d is at negative 1, 1. x-axis, y

Answer 1

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?