Plz
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)

Step-by-step explanation:

A) Triangle PQR is transformed into triangle P'Q'R' by a scale of 1/2 because

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

B) When P'Q'R' reflected across the y axis, the y values don't change, the x values become the opposites, so (-4,0), (-3,1), (1,-2)

C) They are similar, but not congruent. The side length of P''Q''R'' is only half of the side length of PQR. A dilation produces congruent shapes

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4