Answer: The correct option is
(A) Dilation by a scale factor of fraction 1 over 2 followed by reflection about the x-axis.
Step-by-step explanation: We are given to select the set of transformations that has been performed on triangle PQR to form triangle P'Q'R'.
From the graph, we note that
the co-ordinates of the vertices of triangle PQR are P(-4, 2), Q(0, 0) and R(2, 6).
And, the co-ordinates of the vertices of triangle P'QR' are P'(-2, -1), Q'(0, 0) and R'(1, -3).
Let the dilation factor applied on triangle PQR to form triangle P'Q'R' be represented by d.
Then, we observe that
1/2 × P(-4,2)=(-2,1),
1/2 × Q(0,0)=(0,0),
1/2 × R(2,6)=(1,3).
So, the value of d will be
d = 1/2.
Again, to arrive at the vertices of triangle P'Q'R', we need to change the sign before the y co-ordinates ((x, y) ⇒ (x, -y)) of each new vertex hat we found after dilation.
That is,
(-2, 1) ⇒ P'(-2, -1),
(0, 0) ⇒ Q'(0, 0),
(1, 3) ⇒ R'(1, -3).
This is reflection over X-axis.
Therefore, the set of transformation is given by
Dilation by a scale factor of fraction 1 over 2 followed by reflection about the x-axis.
Option (A) is CORRECT.