Respuesta :

Answer:

[tex] T_{-6, 1} \circ r_{x-axis} (x, y) [/tex]

Step-by-step explanation:

We can see in the picture that the first step is transform ABCD to A'B'C'D'. To do this, ABCD is reflected over the x-axis.

Then, A'B'C'D' should be translated -6 units to the right, that is, on the x-axis; and 1 unit up, that is, on the y-axis.

The composition transformation process is from ABCD to A'B'C'D', then

to A''B''C''D''.

Correct response:

  • The composition transformation is; [tex]\underline{T_{-6, \, 1} \ \circ \ r_{x - axis}(x, \, y)}[/tex]

Process used for finding the composition transformation

The given coordinates of the pre-image ABCD are;

A(3, 5), B(6, 5), C(4, 1), D(1, 1).

The coordinates of the image D'C'A'B' are;

A'(3, -5), B'(6, -5), C'(4, -1), and D'(1, -1).

Therefore, the rule that gives the coordinates of A'B'C'D' from ABCD

(x, y) [tex]\underrightarrow{Rule}[/tex] (x, -y)

The rule for a reflection across the x-axis is; (x, y) [tex]\underrightarrow{r_{x-axis}}[/tex] (x, -y)

Therefore;

The rule that gives A'B'C'D', from ABCD is a reflection across the x-axis.

The rule that gives A''B''C''D'' from A'B'C'D' is the a translation 6 units left and 1 unit up, which is; [tex]\mathbf{T_{-6, \, 1}}[/tex]

Therefore composition transformation that maps pre-image ABCD to

final image A''B''C''D'' is given by a reflection followed by a translation,

with the second transformation coming first in the expression as follows;

  • [tex]\underline{T_{-6, \, 1} \ \circ \ r_{x-axis}(x, \, y)}[/tex]

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