Question

The nearest point on the line \( 3x + 4y = 12 \) from the origin is:

• A. \( \left( \frac{36}{25}, \frac{48}{25} \right) \)
• B. \( \left( \frac{3}{5}, \frac{3}{4} \right) \)
• C. \( \left( \frac{2}{3}, \frac{3}{2} \right) \)
• D. None of these

Hint:

Use the perpendicular distance formula to find the closest point from a line to the origin.

Answer 1

The Correct Option is A

Step 1: Use the formula for the distance from a point to a line.
The formula for the perpendicular distance from the origin to the line \( ax + by + c = 0 \) is given by: \[ d = \frac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}} \] Substituting the given equation, the correct coordinates of the nearest point are \( \left( \frac{36}{25}, \frac{48}{25} \right) \).
Thus, the correct answer is (1).