1. **Stating the problem:** We need to find the image (bayangan) of the line given by the equation $x + 2y - 1 = 0$ after a translation by the vector $T\left(-3, 2\right)$. 2. **Formula and explanation:** When a line is translated by a vector $T(h, k)$, the new line has the same slope but its constant term changes. The original line is $x + 2y - 1 = 0$. The translation moves every point $(x, y)$ to $(x', y') = (x + h, y + k)$. Substituting $x = x' - h$ and $y = y' - k$ into the original line equation gives the translated line. 3. **Apply the translation:** Substitute $x = x' - (-3) = x' + 3$ and $y = y' - 2$ into the original equation: $$ (x' + 3) + 2(y' - 2) - 1 = 0 $$ 4. **Simplify:** $$ x' + 3 + 2y' - 4 - 1 = 0 $$ $$ x' + 2y' + (3 - 4 - 1) = 0 $$ $$ x' + 2y' - 2 = 0 $$ 5. **Final answer:** The translated line equation is $$ x + 2y - 2 = 0 $$ 6. **Check options:** None of the options directly match this line equation, but the question asks for the image of the line, which is the line itself shifted. The question's options seem to be points, so we can find the image of a point on the original line to confirm. For example, find the image of the point on the original line when $x=1$: $$ 1 + 2y - 1 = 0 \Rightarrow 2y = 0 \Rightarrow y = 0 $$ Original point: $(1, 0)$ Translated point: $(1 - 3, 0 + 2) = (-2, 2)$ Since the question options are points, the image of the line under translation is the set of points shifted by $(-3, 2)$. The problem's options are points, but none match $(-2, 2)$. Possibly the question has a typo or the vector is $\left(-\frac{3}{2}\right)$ which is incomplete. **Based on the translation vector $T(-3, 2)$, the translated line is:** $$ x + 2y - 2 = 0 $$