Question

Question 2 (10 points) (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)

Answer 1

Answer: From R:(c, d), draw line segment RA perpendicular to the x-axis. Let O denote the origin (0,0).

area ΔPQR = area trapezoid OPRA- area ΔQAR - area ΔOPQ

=

2

1

c(a+d) -

2

1

d(c−b)-

2

1

ab=

2

1

(ac+bd−ab).

If c area ΔPQR = area trapezoid OPRA + area Δ QAR - areaΔOPQ=

2

1

c(a+d)

2

1

d(b−c)−

2

1

ab=

2

1

(ac+bd−ab).

Step-by-step explanation: done