Question

△JKL has vertices J(−3,5), K(−1,0) and L(8,−4). Which of the following represents the translation of △JKL along vector <−4, 7> and its reflection across the x-axis?

Answers:
J (−3, 5) → J ′(1, −2) → J ″(−1, −2);
K (−1, 0) → K ′(3, −7)→ K ″(−3, −7);
L (8, −4)→ L ′(12, −11)→ L ″(−12, −11)


J (−3, 5) → J ′(1, −2) → J ″(1, 2);
K (−1, 0) → K ′(3, −7)→ K ″(3, 7);
L (8, −4)→ L ′(12, −11)→ L ″(12, 11)


J (−3, 5) → J ′(−7, 12) → J ″(7, 12);
K (−1, 0) → K ′(−5, 7)→ K ″(5, 7);
L (8, −4)→ L ′(4, 3)→ L ″(−4, 3)


J (−3, 5) → J ′(−7, 12) → J ″(−7, −12);
K (−1, 0) → K ′(−5, 7)→ K ″(−5, −7);
L (8, −4)→ L ′(4, 3)→ L ″(4, −3)

Answer 1

J (−3, 5) → J ′(−7, 12) → J ″(−7, −12);

K (−1, 0) → K ′(−5, 7)→ K ″(−5, −7);

L (8, −4)→ L ′(4, 3)→ L ″(4, −3)

Step-by-step explantion

Use the translation vector <−4, 7> to determine the rule for translation of the coordinates: (x,y)→(x+(−4),y+7).

Apply the rule to translate vertices J(−3,5), K(−1,0) and L(8,−4).

J(−3,5)→(−3+(−4),5+7)→J'(−7,12).

K(−1,0)→(−1+(−4),0+7)→K'(−5,7).

L(8,−4)→(8+(−4),−4+7)→L'(4,3).

To apply the reflection across x-axis use the rule for reflection: (x,y)→(x,−y).

Apply the reflection rule to the vertices of △J'K'L'.

J'(−7, 12)→J''(−7,−12).

K'(−5,7)→K''(−5,−7).

L'(4,3)→L''(4,−3).

Therefore,

J(−3,5)→J'(−7,12)→J''(−7,−12)K(−1,0)→K'(−5,7)→K''(−5,−7)

L(8,−4)→L'(4, 3)→L''(4,−3)

represents the translation of △JKL along vector <−4, 7> and its reflection across the x-axis.