Triangle pqr is transformed to triangle p'q'r'. triangle pqr has vertices p(3, −6), q(0, 9), and r(−3, 0). triangle p'q'r' has vertices p'(1, −2), q'(0, 3), and r'(−1, 0).

plot triangles pqr and p'q'r' on your own coordinate grid.

part a: what is the scale factor of the dilation that transforms triangle pqr to triangle p'q'r'? explain your answer. (4 points)

part b: write the coordinates of triangle p"q"r" obtained after p'q'r' is reflected about the y-axis. (4 points)

part c: are the two triangles pqr and p''q''r'' congruent? explain your answer. (2 points)

It is very much more instructive if you can visualize the images of triangles PQR, P'Q'R' and P"Q"R".  You can plot this on square paper, or on any technology tool.

On the graph, you can join lines PP', QQ' and RR' to confirm that they meet at the origin O(0,0), which is also the centre of dilation.

Part A
Next, you can compare the lengths OP' and OP using the distance formula, namely mOP'=sqrt(1^2+2^2)=sqrt(5), while mOP = sqrt(3^2+6^2) = sqrt(45) = sqrt(3^2 *5) = 3sqrt(5).

This demonstrate that the scale factor of dilation, equal to mOP'/mOP equals sqrt(5)/3sqrt(5)=1/3.

Try the same with OQ' and OQ, as well as OR' and OR.  You should get the same factor of 1/3.  If not, there is an error in some of the calculations.

Part B: 
Points reflected about the y-axis goes through the transformation as follows:
Sy (x,y) -> (-x,y)
That means you only have to flip the sign of x-coordinate.
For example, P(3,-6) will have its reflection on P"(-3,-6), and so on.

Part C:
PQR and P"Q"R" are congruent because all simple reflections reflected about any line or point conserve the lengths and angles of shapes.

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The answer is 4 points