<h3><u>
We are given:</u></h3>
The initial points: T(2 , 3) U(5, 4) V(2, 0)
The transformed points: T'(-1, 2) U'(2,3) V'(-1, -1)
<h3><u>
Identifying the Transformation rule:</u></h3>
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
<u>Checking if they have a dilation of 0.25 about the origin:</u>
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
<u>Checking if the given points are translated:</u>
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
<u>Change in coordinates of T:</u>
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
<u>Change in coordinates of U:</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
