Question

If IM is reflected across the x-axis and then translated along the vector <4, 1>, in

which quadrant is the final image?

Answer 1

Final image L"M" will lie in the fourth quadrant.

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.