# <span lang="EN-US

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.

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