The given equation of the line is x + 3y = 7
⇒ y = − \(\frac{1}{3}\)x + \(\frac{7}{3}\)
∴ Slope of the line, m1 = – \(\frac{1}{3}\)
Let m2 be the slope of the Perpendicular.
∴ m1 m2 = – 1
⇒ − \(\frac{1}{3}\) × m2 = − 1
⇒ m2 = 3.
∴ Equation of the perpendicular line with slope 3 and passing through (3, 8) is
y – 8 = 3 (x – 3)
⇒ 3x – y – 1 = 0
∴ The foot of the perpendicular is the point intersection of the lines x + 3y – 7 = 0 and 3x – y – 1 = 0
Solving these equations, we get
x = 1, y = 2, so (1, 2) is the foot of the perpendicular.