Answer:
X (15, −8) → X ′(9, −3) → X ″(9, 3);
Y (13, 21) → Y ′(7, 26) → Y ″(7, −26);
Z (−17, 17) → Z ′(−23, 22) → Z ″(−23, −22)
Explanation:
Use the translation vector <−6, 5> to determine the rule for translation of the coordinates: (x, y)→ (x+(−6),y + 5).
Apply the rule to translate vertices X(15 ,−8), Y(13, 21) , and Z(−17, 17) .
X (15,−8) → (15 + (−6),−8 + 5) → X'(9, −3).
Y (13, 21) → (13+ (−6), 21 + 5) → Y' (7, 26).
Z (−17, 17) → (−17 + (−6), 17 + 5) → Z' (−23, 22).
To apply the reflection across x-axis use the rule for reflection: (x, y) → (x, −y).
Apply the reflection rule to the vertices of △X'Y'Z'.
X' (9, −3) → X'' (9, 3).
Y' (7, 26)→Y''(7, −26).
Z' (−23, 22) → Z'' (−23, −22).
Therefore,
X (15 ,−8) → X' (9, −3) → X'' (9, 3)
Y (13, 21) → Y' (7, 26) → Y'' (7, −26)
Z (−17, 17) → Z' (−23, 22) → Z'' (−23, −22)
represents the translation of △XYZ along vector <−6, 5> and its reflection across the x-axis.