Class 10
MATHS
Coordinate Geometry

# Find the coordinates of the point R on the line segment joining the points P(-1,3) and Q (2,5) such that PR =(3)/(5) PQ.

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Updated On: 29-8-2020

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Solution :
According to the question , <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/ARH_NCERT_EXE_MATH_X_C07_S01_050_S01.png" width="80%"> <br> Given that , PR =(3)/(5)PQ <br> rArr(PQ)/(PR)=(5)/(3) <br> rArr(PR+RQ)/(PR)=(5)/(3) <br> rArr1+(RQ)/(PR)=(5)/(3) <br> rArr(PQ)/(PR)=(5)/(3)-1=(2)/(3) <br> :. PQ :PR= 2 : 3 <br> or :. PR:RQ = 3 : 2 <br> Suppose , R (x,y) be the point which divides the line segment joining the points P (-1,3) and Q(2,5) in the ration 3 : 2. <br> :. (x,y) ={(3(2)+2(-1))/(3+2),(3(5)+2(3))/(3+2)} <br> [:' by internal section formula , :. (x,y) ={(m_(2)x_(1)+m_(1)x_(2))/(m_(1)+m_(2)),(m_(2)y_(1)+m_(1)y_(2))/(m_(1)+m_(2))}] <br> =((6-2)/(5),(15+6)/(5))=((4)/(5),(21)/(5)) <br> Hence , the required coordinates of the point R is ((4)/(5),(21)/(5)).

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