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The hypotenuse of a right angles has its ends at the points (1, 3)and (– 4, 1). Find the equation of the perpendicular sides of the triangle.

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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.

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