Question

Find the coordinates of the point which divides the line segment joining the points A(4, –3)

and B(9, 7) in the ration 3 : 2​

Answer 1

Step-by-step explanation:

Given :-

Points A(4, –3) and B(9, 7)

To find :-

Find the coordinates of the point which divides the line segment joining the points A(4, –3) and B(9, 7) in the ratio

3 : 2?

Solution:-

Given points are A(4, –3) and B(9, 7)

Let (x1, y1) = (4,-3) => x1 = 4 and y1 = -3

Let (x2, y2) = (9,7) => x2 = 9 and y2 = 7

Given ratio = 3:2

Let m1:m2 = 3:2 => m1 = 3 and m2 = 2

We know that

The coordinates of the point P(x,yl which divides the line segment joining the points (x1, y1) and (x2, y2) in the ratio m1:m2 is P(x,y) =

({m1x2+m2x1}/(m1+m2),{m1y2+m2y1}/(m1+m2) )

On Substituting these values in the above formula then

=> ( {(3)(9)+(2)(4)}/(3+2),{(3)(7)+(2)(-3)}/(3+2) )

=> ( {27+8}/5 , ({21-6}/5 )

=> ( 35/5 , 15/5 )

=> (7,3)

Therefore, P(x,y) = (7,3)

Answer:-

The coordinates of the point which divides the linesegment joining the given points is (7,3)

Used formulae:-

Section formula:-

The coordinates of the point P(x,yl which divides the line segment joining the points (x1, y1) and (x2, y2) in the ratio m1:m2 is P(x,y) =

({m1x2+m2x1}/(m1+m2) , {m1y2+m2y1}/(m1+m2) )