Which set of transformations has been performed on triangle pqr to form triangle p'q'r'? a. dilation by a scale factor of fraction 1 over 2 followed by reflection about the x-axis b. dilation by a scale factor of 2 followed by reflection about the x-axis c. dilation by a scale factor of fraction 1 over 2 followed by reflection about the y-axis d. dilation by a scale factor of 2 followed by reflection about the y-axis

 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.