Question

The coordinates of the foot of perpendicular from the point \( (2, 3) \) on the line \( y = 3x + 4 \) is given by:

• A. \( \left( \frac{37}{10}, \frac{-1}{10} \right) \)
• B. \( \left( \frac{-1}{10}, \frac{37}{10} \right) \)
• C. \( \left( \frac{10}{37}, -10 \right) \)
• D. \( \left( \frac{2}{2}, \frac{-1}{3} \right) \)

Hint:

For finding the foot of the perpendicular from a point to a line, use the slope condition \( m_1 \times m_2 = -1 \) and the fact that the foot of the perpendicular lies on the given line.