Graph TU with endpoints T(1,2) and U(4,6) and its image after the composition.
Translation: (x, y) → (x-2, y-3)
Translation: (x, y) → (x-4, y + 5)

The graph of the line segment after the translation (x, y) → (x-2, y-3) and (x, y) → (x-4, y + 5) has been drawn.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

As per the given coordinate,T(1,2) and U(4,6)

Apply the translation (x, y) → (x-2, y-3)

T(1,2) → T'(1 - 2,2 - 3) = T'(-1,-1)

U(4,6) →  U'(4 - 2,6 - 3) = U'(2,3).

Apply the translation (x, y) → (x-4, y + 5)

T(1,2) → T'(1 - 4,2 + 5) = T'(-3,7)

U(4,6) →  U'(4 - 4,6 + 5) = U'(0,11)

All points have been plotted below.

Hence"After the translations (x, y) → (x-2, y-3)  and (x, y) → (x-4, y + 5), the graph of the line segment has been drawn.".

To learn more about the transformation of graphs,

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Answer:

Translation (x, y) → (x - 2, y - 3):

Translation (x, y) → (x - 4, y + 5):

Step-by-step explanation:

Given endpoints of line segment TU:

Translation 1 (blue on attached diagram)

This means to subtract 2 from the x-values of the endpoints, and subtract 3 from the y-values of the endpoints:

Therefore:

Translation 2 (red on attached diagram)

This means to subtract 4 from the x-values of the endpoints, and add 5 to the y-values of the endpoints:

Therefore:

Graph y=0.4x.........................................

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