Triangle PQR with vertices P(3, −6), Q(6, −9), and R(−15, 3) is dilated by a scale factor of 3 to obtain triangle P′Q′R′. Which statement best describes triangle P′Q′R′? (5 points)
It is similar to triangle PQR and has coordinates P′(1, −2), Q′(2, −3), and R′(−5, 1).
It is congruent to triangle PQR and has coordinates P′(1, −2), Q′(2, −3), and R′(−5, 1).
It is similar to triangle PQR and has coordinates P′(9, −18), Q′(18, −27), and R′(−45, 9).
It is congruent to triangle PQR and has coordinates P′(9, −18), Q′(18, −27), and R′(−45, 9).
To find the coordinates of the vertices of triangle P'Q'R' after the dilation, we multiply the x-coordinates and y-coordinates of each vertex of triangle PQR by the scale factor of 3.
P' = (3 * 3, -6 * 3) = (9, -18)
Q' = (6 * 3, -9 * 3) = (18, -27)
R' = (-15 * 3, 3 * 3) = (-45, 9)
Since the coordinates of the vertices are (9, -18), (18, -27), and (-45, 9), the triangle P'Q'R' is congruent to triangle PQR.
Therefore, the correct answer is:
It is congruent to triangle PQR and has coordinates P′(9, −18), Q′(18, −27), and R′(−45, 9).