Question

Identify the translation of the figure with the vertices P(−4,−5), L(1,−7), and K(−9,8), along the vector <−6, 3>.

Answers:
P ′(−10, −2), L ′(−5, −4), K ′(−15, 11)
P ′(2, −8), L ′(7, −10), K ′(−3, 5)
P ′(−10, −8), L ′(−5, −10), K ′(−15, 5)
P ′(2, −2), L ′(7, −4), K ′(−3, 11)

Answer 1

P ′(−10, −2), L ′(−5, −4), K ′(−15, 11)

Explanation:

P(−4,−5)→P'(−10,−2)

L(1,−7)→L'(−5,−4)

K(−9,8)→K'(−15,11)

Therefore, P'(−10,−2), L'(−5,−4), N'(−15,11) is the translation of the figure with the vertices P(−4,−5), L(1,−7), and K(−9,8), along the vector ⟨−6,3⟩.

Answer 2

P ′(−10, −2), L ′(−5, −4), K ′(−15, 11)

Explanation:

The translation vector, ⟨−6,3⟩, can be used to derive a rule for the translation of the coordinates: (x,y)→(x−6,y+3).

Apply the rule to translate each of the three preimage vertices to the image vertices.

P(−4,−5)→P'(−10,−2)

L(1,−7)→L'(−5,−4)

K(−9,8)→K'(−15,11)

Therefore, P'(−10,−2), L'(−5,−4), N'(−15,11) is the translation of the figure with the vertices P(−4,−5), L(1,−7), and K(−9,8), along the vector ⟨−6,3⟩.