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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)

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maniknandini maniknandini · Answer 1 · 2021-11-16T23:54:38+01:00

Answer:

see below

Step-by-step explanation:

see the picture below red one is ΔPQR

blue one is ΔP'Q'R'

green one is ΔP''Q''R''

Part A:

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).

(8,0) ---> (4,0) --> 8/2, 0/2

(6,2) ----> (3,1) --> 6/2, 2/2

(-2,-4) -----> (-1,-2) ---> -2/2, -4/2

so the scale factor is 1/2

Part B:

to reflect about y axis , point (x, y) becomes (-x, y)

so P'' is (-4,0)

Q'' is (-3, 1)

R'' is (1, -2)

Part C:

PQR and P''Q''R'' have same shape means same angles

but not the same size as it is dilated

so they are not congruent