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ICSE Class 10 Answered

FIND THE COORDINATES OF THE FOOT OF THE PERPENDICULAR DROPPED FROM THE POINT (3,2) TO THE LINE PASSING THROUGH THE POINTS (-1,-2) AND (4,-3)
Asked by aniketmeena2000 | 07 Jan, 2019, 06:49: PM
answered-by-expert Expert Answer
Equation of the line passing through (-1, -2) and (4,-3) is given by
 
begin mathsize 12px style fraction numerator y plus 2 over denominator negative 2 plus 3 end fraction equals fraction numerator x plus 1 over denominator negative 1 minus 4 end fraction space space o r space space y space equals space minus x over 5 minus 11 over 5 space space.............. left parenthesis 1 right parenthesis end style
Hence slope of this line is -1/5  and slope of the perpendicular line = 5
 
let the perpendicular line is y = 5x+C  and it is passing through (3,2 ) . hence 2 = 15+C   or C = -13
 
Hence perpendicular line  : y = 5x-13  ...........(2)
 
by solving eqns.(1) and (2), we get the coordinates of foot of perpendicular as { (27/13), -34/13 }
Answered by Thiyagarajan K | 08 Jan, 2019, 12:13: PM

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