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)

The correct answers are:

1/3; P''(-1, -2), Q''(0, 3), R''(1, 0); and No.

Explanation:

To find the scale factor, we must find the length of a side from the pre-image and one from the image.  We will use the distance formula for this.

For PQ,

For P'Q',

The length of P'Q' is 1/3 the length of PQ, so the scale factor is 1/3.

Reflecting P'Q'R' across the y-axis negates each x-coordinate.  This gives us

P'(1, -2)→P''(-1, -2)

Q'(0, 3)→Q''(0, 3)

R'(-1, 0)→R''(1, 0)

The two triangles are not congruent; this is because the lengths of the sides are not the same.  In order for two triangles to be congruent, the sides and angles must be the same in the two triangles.

Scale factor for dilation is 1/2 or 0.5

because 1/2 (8,0) = (4,0) ; 1/2(6,2) =(3,1) ; 1/2(-2,-4) = (-1,-2)

If P'Q'R' is reflected in y axis x coordinate will be same but y coordinate will be negatived

P" ( 4,0)

Q" (3,-1)

R"(-1,2) 

The triangle is reflected. the sides are equal. Areas are equal.

Distance between (4,0) and (3,-1) = sqrt[(4-3)^2+(0-(-1))^2] = sqrt[1+1] =sqrt (2)

In the other triangle distance between (4,0) and (3,1) =sqrt[(4-3)^2+(0-1)^2] =sqrt(1+1) =sqrt(2)

and so on.

y= -