(02.05 MC) Triangle PQR is transformed to triangle P'Q'R'. Triangle PQR has vertices P(8, 0), Q(6, 2), and R(−2, −4). Triangle P'Q'R' has vertices P'(4, 0), Q'(3, 1), and R'(−1, −2). 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)

Part A. I believe the scale factor of the dilation is 1/2 because since P'Q'R' becomes smaller than PQR, the scale factor must be less than 1. Also, the coordinates P(8,0) and P'(4,0) when the x coordinate of P is multiplied by something to get 4, we find that the something is 1/2 (8 times ? = 4).

Part B.- P''(-4,0)  Q''(-3,1)    R''(1,-2)

Part C: First, find the distance between P'' and Q'' using the distance formula:

the sq. rt (-3 + 4)^2 + (1 - 0)^2 = the sq. rt of 1 + 1 or the sq. rt of 2

Now find the distance between R'' and Q'':

the sq. rt (-3 - 1)^2 + (1 + 2)^2 = the sq. rt of 16 + 9 = the sq. rt of 25 or 5.

Now find the distance between P and Q:

the sq. rt of 4 + 4 = the sq rt of 8

Now find the distance between Q and R:

the sq. rt 64 + 36 = the sq. rt of 100 = 10

Now see if the side lengths are in equal proportion:

5/10      the sq. rt of 8/the sq. rt of 2

0.5             2

The two triangles are not congruent.

the answer is 13

step-by-step explanation:

5*5=25

12*12=144

25+144=169

169^2=13