Q. 105.0( 2 Votes )

Find the distance of the point (1, 2) from the straight line with slope 5 and passing through the point of intersection of x + 2y = 5 and x – 3y = 7.

Answer :

Given:


Lines x + 2y = 5 and x – 3y = 7, slope = 5.


To find:


The distance of the point (1, 2) from the straight line with slope 5 and passing through the point of intersection of x + 2y = 5 and x – 3y = 7.


Concept Used:


Distance of a point from a line.


Explanation:


To find the point intersection of the lines x + 2y = 5 and x 3y = 7, let us solve them.



x y


So, the equation of the line passing through with slope 5 is



5y + 2 = 25x – 145


25x – 5y – 147 = 0


Let d be the perpendicular distance from the point (1, 2) to the line 25x – 5y – 147 = 0


d


Hence, the required perpendicular distance is


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