1. **Problem statement:** Find the distance between the two parallel lines given by the equations $$4x + 3y - 2 = 0$$ and $$4x + 3y + 8 = 0$$.
2. **Formula used:** The distance $d$ between two parallel lines $$Ax + By + C_1 = 0$$ and $$Ax + By + C_2 = 0$$ is given by:
$$
d = \frac{|C_2 - C_1|}{\sqrt{A^2 + B^2}}
$$
3. **Identify coefficients:** For both lines, $A = 4$, $B = 3$, $C_1 = -2$, and $C_2 = 8$.
4. **Calculate numerator:**
$$|C_2 - C_1| = |8 - (-2)| = |8 + 2| = 10$$
5. **Calculate denominator:**
$$\sqrt{A^2 + B^2} = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5$$
6. **Calculate distance:**
$$d = \frac{10}{5} = 2$$
7. **Answer:** The distance between the two lines is $2$.
Therefore, the correct choice is (c) 2.
Distance Parallel 72C31D
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