(Please this is URGENT!) On a computer screen, Jennifer just created a triangular design of a banner with vertices at A(-4,3), B(-1,5) and C(-1,2). She can use the computer software to perform transformations on this design.

Which sequence of two transformations could she perform so that the transformed vertices become A'(4,-5), B'(7,-7), and C'(7,-4)?

a. translating 6 units down, followed by translating 8 units to the right

b. reflecting about the line y = -2, followed by translating 8 units to the right

c. reflecting about the line y = -1, followed by reflecting about the y-axis

d. reflecting about the line y = -1, followed by translating 8 units to the right

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Respuesta :

puchi2005 puchi2005 · Answer 1 · 2020-12-09T15:52:08+01:00

Answer:

The answer is D

Step-by-step explanation:

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MrRoyal MrRoyal · Answer 2 · 2021-12-11T06:26:41+01:00

Transformation involves changing the position of points in the coordinate plane

The sequence of two transformations is (d) reflecting about the line y = -1, followed by translating 8 units to the right

The vertices of ABC are given as

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

[tex]B = (-1,5)[/tex]

[tex]C = (-1,2)[/tex]

First the vertices of ABC are reflected across the line y = -1.

The rule of this transformation is:

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

So, the vertices of ABC after reflection across the line y = -1 are

[tex]A = (-4,-5)[/tex]

[tex]B = (-1,-7)[/tex]

[tex]C = (-1,-4)[/tex]

Next, the vertices are shifted 8 units right.

The rule of this transformation is:

[tex](x,y) \to (x + 8,y)[/tex]

So, the vertices of ABC after this horizontal shift are

[tex]A' = (-4 + 8,-5)[/tex]

[tex]A' = (4,-5)[/tex]

[tex]B' = (-1 + 8,-7)[/tex]

[tex]B' = (7,-7)[/tex]

[tex]C' = (-1 + 8,-4)[/tex]

[tex]C' = (7,-4)[/tex]

Hence, the sequence of transformation is (d)