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. Group of answer choices x-axis, y=x, y-axis, x-axis x-axis, y-axis, x-axis y=x, x-axis, x-axis y-axis, x-axis, y-axis, x-axis

Answer 1

Answer:

y=x, x axis,  y=x, y axis

Step-by-step explanation:

If a point A(x, y) is reflected along the y = x line, the new coordinates would be A'(y, x)

If a point A(x, y) is reflected across the x axis, the new coordinates would be A'(x, -y)

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

Firstly reflect Trapezoid ABCD along the y = x line to give:

A (-5, 1) ⇒ A'(1, -5). B (-4, 3) ⇒ B'(3, -4). C (-2, 3) ⇒C'(3, -2). D (-1, 1) ⇒ D'(1, -1)

Secondly reflect along the x axis to give:

A'(1, -5)⇒ A"(1,5). B'(3, -4)⇒ B"(3,4), C'(3, -2)⇒C"(3, 2), D'(1, -1) ⇒ D"(1, 1)

Thirdly reflect along the y = x line to give:

A"(1,5) ⇒ A"'(5, 1). B"(3,4) ⇒ B"'(4, 3). C"(3, 2) ⇒ C"'(2, 3). D"(1, 1) ⇒ D"'(1, 1)

Lastly reflect along the y axis to give:

A"'(5, 1) ⇒ A""(-5, 1), B"'(4, 3) ⇒ B""(-4, 3), C"'(2, 3) ⇒ C""(-2, 3), D"'(1, 1) ⇒ D""(-1.1)