Question

the line Ax + By + C = 0 will always be perpendicular to the line Bx - Ay + C = 0
Is this method reasonable? explain why or why not

Answer 1

Product of their slopes is -1. Hence the lines are perpendicular to each other.

Step-by-step explanation:

Given: Two lines Ax + By + C = 0 and Bx - Ay + C = 0.

Prove: They are perpendicular.

Solution: Let's write the line equation in the form y = mx + c where m is the slope.

Ax + By + C = 0

Ax + C = -By

y = -A/B x - C/B where slope is m1 = -A/B

Now  Bx - Ay + C = 0.

  Bx + C = Ay

  y = B/A x + CA where slope is m2 = B/A

The two lines will be perpendicular when the product of their slopes is -1.

m1*m2 = -A/B * B/A = -1

Hence proved.