Given △ABC with coordinates A(1, 3), B(4, 5), and C(5, 2), what are the coordinates of △AʹBʹCʹ after the glide reflection described by T⟨−1, 1⟩° Ry-axis?

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hopetran775 hopetran775 · Answer 1 · 2021-01-17T14:09:18+01:00

Answer:

A' = ( 0,4 )

B' = ( -3,6 )

C' = ( -4,3 )

Step-by-step explanation:

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MrRoyal MrRoyal · Answer 2 · 2021-12-21T11:53:37+01:00

Transformation involves changing the coordinates of a shape.

The coordinates of △ABC after the glide transformation are [tex]A' = ( 0,4 )[/tex], [tex]B' = ( -3,6 )[/tex] and [tex]C' = ( -4,3 )[/tex]

The coordinates of triangle ABC is given as:

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

[tex]B = (4,5)[/tex]

[tex]C = (5,2)[/tex]

The glide reflection is given as: T⟨−1, 1⟩° Ry-axis

So, we start by translating the shape by (x - 1, y + 1).

The coordinate ABC becomes

[tex]A = (1 - 1, 3 + 1) = (0,4)[/tex]

[tex]B = (4 - 1, 5 + 1) = (3,6)[/tex]

[tex]C = (5 - 1, 2 + 1) = (4,3)[/tex]

Next, we reflect the coordinates across the y-axis.

The rule of this reflection is:

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

So, we have:

[tex]A' = ( 0,4 )[/tex]

[tex]B' = ( -3,6 )[/tex]

[tex]C' = ( -4,3 )[/tex]