to

T '(-1, 2), U '(2, 3), V '(-1, -1)

a. dilation of .25 about the origin

b. translation: (x, y)LaTeX: \longrightarrow⟶(x - 3, y)

c. reflection across the y-axis

d. translation: (x, y)LaTeX: \longrightarrow⟶(x - 3, y - 1)

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T(2, 3), U(5, 4), V(2, 0)

to

T '(-1, 2), U '(2, 3), V '(-1, -1)

a. dilation of .25 about the origin

b. translation: (x, y)LaTeX: \longrightarrow⟶(x - 3, y)

c. reflection across the y-axis

d. translation: (x, y)LaTeX: \longrightarrow⟶(x - 3, y - 1)

to

T '(-1, 2), U '(2, 3), V '(-1, -1)

a. dilation of .25 about the origin

b. translation: (x, y)LaTeX: \longrightarrow⟶(x - 3, y)

c. reflection across the y-axis

d. translation: (x, y)LaTeX: \longrightarrow⟶(x - 3, y - 1)

The initial points: T(2 , 3) U(5, 4) V(2, 0)

The transformed points: T'(-1, 2) U'(2,3) V'(-1, -1)

Since all these points will follow the same rule, we will take a pair of initial and transformed points and compare them

T(2, 3) → T'(-1, 2)

We can see that these points are **not reflected across the y-axis**

__Checking if they have a dilation of 0.25 about the origin:__

Dilation of 0.25 about the origin basically means if the Initial x and y coordinates are multiplied by 0.25 to form the transformed points

So, if the points have a dilation of 0.25:

x (initial) * 0.25 = x(final)

2*0.25 = -1

0.5 ≠ -1

Hence, **there is no dilution of 0.25**

__Checking if the given points are translated:__

To check this, we will take 2 pairs of initial and transformed points

T(2,3) → T'(-1,2)

U(5,4) → U'(2,3)

To check if there is transformation, we need to check if the difference between the x and y coordinates of initial and transformed points is equal

__Change in coordinates of T:__

x-coordinates:

x(final) - x(initial) = x(change)

x(change) = -1 - (2)

**x(change) = -3**

y-coordinates:

y(change) = y(final) - y(initial)

y(change) = 2 - (3)

**y(change) = -1**

__Change in coordinates of U:__

x-coordinates:

x(change) = x(final) - x(initial)

x(change) = 2 - 5

**x(change) = -3**

y-coordinates:

y(change) = y(final) - y(initial)

y(change) = 3 - 4

**y(change) = -1**

**Since there is the same change in x and y coordinates of the initial and transformed points, we know that Translation took place**

Since the change in x is -3 and the change in y is -1, the translation will look like:

**(x-3 , y-1)**

Which is also option d.

**Hence, option d is the correct answer**

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