Answer :

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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