Question

The coordinates of the foot of the perpendicular from the point (2, 3) on the line x + y – 11 = 0 are
(a) (–6, 5)
(b) (5, 6)
(c) (–5, 6)
(d) (6, 5)

Answer 1

For given line say CD; x + y – 11 = 0

Slope is given by $\frac{-1}{1}=-1$
Since AB is perpendicular to CD
Slope AB = $\frac{-1}{\mathrm{slope}\mathrm{of}CD}$
Slope of AB = 1
∴ equation of AB is y – 3 = + 1(x – 2)
i.e. y – 3 = x – 2
i.e. x – y + 1 = 0
∴ Coordinates of B is given by point of intersection of AB and CD.
i.e. x + y – 11 = 0
$$\begin{gathered} \frac{x-y+1=0}{2x-10=0} \\ x=5 \\ y=6 \end{gathered}$$
i.e. Coordinates of foot of perpendicular from (2, 3) to x + y – 11 = 0 is (5, 6)

Hence, the correct answer is option B.