Given:

Lines 2x – 3y + 14 = 0 and 5x + 4y – 7 = 0.

To find:

The length of the perpendicular from the point (4, -7) to the line joining the origin and the point of intersection of the lines 2x – 3y + 14 = 0 and 5x + 4y – 7 = 0.

Concept Used:

Distance of a point from a line.

Explanation:

Solving the lines 2x − 3y + 14 = 0 and 5x + 4y − 7 = 0 we get:

⇒ x, y

So, the point of intersection of 2x − 3y + 14 = 0 and 5x + 4y − 7 = 0 is

The equation of the line passing through the origin and the point is

⇒ y

⇒ y

⇒ 12x + 5y = 0

Let d be the perpendicular distance of the line 12x + 5y = 0 from the point (4, − 7)

∴d

Hence, Length of perpendicular is 1.