Reduce the lines 3x – 4y + 4 = 0 and 2x + 4y – 5 = 0 to the normal form and hence find which line is nearer to the origin.

Question

Philoid · Accepted Answer

Given:

The normal forms of the lines 3x − 4y + 4 = 0 and 2x + 4y − 5 = 0.

To find:

In given normal form of a line, Which is nearer to the origin.

Explanation:

Dividing both sides by

…… (1)

Now 2x + 4y = - 5

⇒ - 2x – 4y = 5

Dividing both sides by

…… (2)

From equations (1) and (2):

45<525

Hence, the line 3x − 4y + 4 = 0 is nearer to the origin.