Q3 of 53 Page 115

Find the ratio in which point T(-1, 6)divides the line segment joining the pointsP(-3, 10) and Q(6, -8).

A point P(x,y) divides the line formed by points (a,b) and (c,d) in the ratio of m:n, then the coordinates of the point P is given by


and


In the given question,


Let the point T divide the line PQ in the ratio m:n


Here x = -1 and y = 6


...(1)


.... (2)


Simplifying (1) we get,


-m-n = -3n + 6m


2n = 7m


Simplifying (2) we get,


6m + 6n = 10n-8m


14m = 4n


From both we get


Hence the point T divides PQ in the ratio 2:7


More from this chapter

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1

Find the coordinates of point P if P divides the line segment joining the points A(-1,7) and B(4,-3) in the ratio 2:3.

 2

In each of the following examples find the co-ordinates of point A which divides segment PQ in the ratio a:b.

(1) P(-3, 7), Q(1, -4), a:b = 2:1


(2) P(-2, -5), Q(4, 3), a:b = 3:4


(3) P(2, 6), Q(-4, 1), a:b = 1:2

 4

Point P is the centre of the circle and AB is a diameter. Find the coordinates ofpoint B if coordinates of point A and P are (2, -3) and (-2, 0) respectively.

 5

Find the ratio in which point P(k, 7) divides the segment joining A(8, 9) andB(1, 2). Also find k.