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ICSE Class 10 Answered

find the ratio in which the line segment joining the points (2, 3) and (4, 5) is divided by the lin joining (6, 8) and (-3, 2)
Asked by Ganga | 18 Dec, 2018, 04:23: PM
answered-by-expert Expert Answer
Equation of line segment joining points P(2,3) and Q(4,5) : begin mathsize 12px style fraction numerator x minus 2 over denominator 2 minus 4 end fraction space equals space fraction numerator y minus 3 over denominator 3 minus 5 end fraction space space o r space x minus y space equals space minus 1 space space............... left parenthesis 1 right parenthesis end style
Equation of line passing through points (-3,2) and (6,8) : begin mathsize 12px style fraction numerator x plus 3 over denominator negative 3 minus 6 end fraction space equals space fraction numerator y minus 2 over denominator 2 minus 8 end fraction space o r space 2 x space minus space 3 y space equals space minus 12 space............. left parenthesis 2 right parenthesis end style
Let R be the point of intersection of both the lines.
Coordinates of point of intersection are obtained by solving eqn.(1) and eqn.(2).
 
After solving eqn.(1) and eqn.(2), we get coordinates of point of intersection as (9, 10).
 
It can be seen that point of intersection does not lie between points P(2,3) and Q(4,5).
Hence the line segment is divided by point R externally.
 
Let the external division ratio is given as PR : QR = m : n
 
then using x-coordinates, we have begin mathsize 12px style fraction numerator m cross times 4 space minus space n cross times 2 over denominator m minus n end fraction space equals space 9 space space space o r space 5 m minus 7 n space equals space 0 space space space o r space m colon n space equals space 7 colon 5 end style
Similarly by using y-coordinates, we get m:n = 7:5
Answered by Thiyagarajan K | 18 Dec, 2018, 10:30: PM
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