Show that the line joining (2, – 5) and (– 2, 5) is perpendicular

1.	Show that the line joining (2, – 5) and (– 2, 5) is perpendicular to the line joining (6, 3) and (1,1).
Answer» To Prove: The Given line is perpendicular to each other. Proof: Let Assume the coordinate A(2, – 5) and B(– 2, 5) joining the line AB, C(6,3) and D(1,1) joining the line CD. The concept used: The product of the slopes of lines always – 1. The formula used: The slope of the line, m = \(\frac{y_2-y_1}{x_2-x_1}\) Now, The slope of AB = \(\frac{5-(-5)}{-2-2}\) The Slope of AB = \(\frac{10}{-4}\) Now, The slope of CD = \(\frac{1-3}{1-6}\) The Slope of AB = \(\frac{2}{5}\) So, AB × CD = \(\frac{10}{-4}\times\frac{2}{5}\) AB × CD = – 1 Hence, The given Lines are perpendicular to each other.

Show that the line joining (2, – 5) and (– 2, 5) is perpendicular to the line joining (6, 3) and (1,1).

Answer»

To Prove: The Given line is perpendicular to each other.

Proof: Let Assume the coordinate A(2, – 5) and B(– 2, 5) joining the line AB, C(6,3) and D(1,1) joining the line CD.

The concept used: The product of the slopes of lines always – 1.

The formula used: The slope of the line, m = \(\frac{y_2-y_1}{x_2-x_1}\)

Now, The slope of AB = \(\frac{5-(-5)}{-2-2}\)

The Slope of AB = \(\frac{10}{-4}\)

Now, The slope of CD = \(\frac{1-3}{1-6}\)

The Slope of AB = \(\frac{2}{5}\)

So, AB × CD = \(\frac{10}{-4}\times\frac{2}{5}\)

AB × CD = – 1

Hence, The given Lines are perpendicular to each other.