Answer:
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.
