Question

DUE: 10-31-2019
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.

Answer 1

Answer:

Here's what I get  

Step-by-step explanation:

I plotted the triangles in the diagram below.

Part A

The scale factor for dilation is ½, because every coordinate has been halved.

  P (8, 0) ⟶ P' (4, 0)

  Q (6, 2) ⟶ Q' (3, 1)

R (-2, -4) ⟶ R' (-1, -2)

Part B

When you reflect a point (x, y) about the y-axis, the y-coordinate remains the same, but the x-coordinate gets the opposite sign. Thus,

  P' (4,0) ⟶ P" (-4,0)

Q' (3,-1) ⟶ Q" (-3,-1)

R' (-1,-2) ⟶ R" (1,-2)

∆P"Q"R" has coordinates P" (-4,0), Q" (-3,-1), R"(1,-2).

Part C

∆PQR and ∆ P"Q"R" are not congruent, because corresponding sides are not equal.