# Show that the origin is equidistant from the lines 4x + 3y + 10 = 0; 5x – 12y + 26 = 0 and 7x + 24y = 50.

Given: The lines 4x + 3y + 10 = 0; 5x – 12y + 26 = 0 and 7x + 24y = 50.

To prove:

The origin is equidistant from the lines 4x + 3y + 10 = 0; 5x – 12y + 26 = 0 and 7x + 24y = 50.

Explanation:

Let us write down the normal forms of the given lines.

First line: 4x + 3y + 10 = 0

- 4x - 3y = 10

Dividing both sides by

p = 2

Second line: 5x − 12y + 26 = 0

- 5x + 12y = 26

Dividing both sides by

p = 2

Third line: 7x + 24y = 50

Dividing both sides by

p = 2

Hence, the origin is equidistant from the given lines.

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