Answer:
Final image L"M" will lie in the fourth quadrant.
Step-by-step explanation:
Coordinates of the ends of segment LM,
L → (-3, 4)
M → (-3, 2)
Rule to reflect a point across x-axis is,
(x, y) → (x, -y)
By this rule, coordinates of the image point of L and M will be,
L(-3, 4) → L'(-3, -4)
M(-3, 2) → M'(-3, -2)
Further these image points are translated along the vector <4, 1>
Rule for this translation will be,
(x, y) → (x + 4, y + 1)
Now the image points of the points L' and M' will be,
L'(-3, -4) → L"(-3 + 4, -4 + 1)
→ L"(1, -3)
M'(-3, -2) → M"(-3 + 4, -2 + 1)
→ M"(1, -1)
Therefore, final image L"M" will lie in the fourth quadrant.
