Which transformation carries the trapezoid onto itself?

only a rotation of 360° about any point will carry each trapezoid onto itself, the nonisosceles trapezoid has no lines of reflection, and the isosceles trapezoid has only one - the line that contains the midpoints of the two parallel sides.

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MrRoyal MrRoyal · Answer 2 · 2021-12-13T14:27:21+01:00

Transformation involves changing the position of a shape.

The transformation that carries the trapezoid onto itself is a reflection across the line x = -1

The coordinates of the trapezoid (see attachment) are:

[tex]A = (-3,3)[/tex]

[tex]B = (1,3)[/tex]

[tex]C = (3,-3)[/tex]

[tex]D = (-5,-3)[/tex]

The transformation rule of a reflection across the line x = -1 is:

[tex](x,y) \to (-x-2,y)[/tex]

So, we have:

[tex]A' = (3-2,3)[/tex]

[tex]A' = (1,3)[/tex]

[tex]B' = (-1-2,3)[/tex]

[tex]B' = (-3,3)[/tex]

[tex]C' = (-3-2,-3)[/tex]

[tex]C' = (-5,-3)[/tex]

[tex]D' = (5-2,-3)[/tex]

[tex]D' = (3,-3)[/tex]

Comparing the coordinates of the trapezoid before and after the transformation, we have:

[tex]A = (-3,3)[/tex] [tex]B' = (-3,3)[/tex]

[tex]B = (1,3)[/tex] [tex]A' = (1,3)[/tex]

[tex]C = (3,-3)[/tex] [tex]D' = (3,-3)[/tex]

[tex]D = (-5,-3)[/tex] [tex]C' = (-5,-3)[/tex]

Hence, the transformation that carries the trapezoid onto itself is a reflection across the line x = -1