Let us plot the points A(1, 3) and B(– 4, 1) in the XY-plane. From A(1, 3), we draw a line parallel to y-axis and from B(– 4, 1), we draw a line parallel to x-axis. These two lines meet at C, which is the right angle of ∆ABC.
CO-ordinate of C are (1, 1)
Now, Equation of the line passing through B(– 4, 1) and C(1, 1) is given by
y − 1 = \(\frac{1 − 1}{1 + 4}\)(x + 4)
⇒ y = 1
and equation of the line passing through A(1, 3) and B(1, 1) is given by
y − 1 = \(\frac{1 − 3}{1 - 1}\)(x − 1)
⇒ x = 1
∴ Equation of the two perpendicular lines are x = 1 and y = 1.