Question

If the point C(k,4) divides the line segment joining two points A(2,6) and B(5,1) in ratio 2 : 3, then find the value of k

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Answer 1

Step-by-step explanation:

Given:-

the point C(k,4) divides the line segment joining two points A(2,6) and B(5,1) in ratio 2 : 3.

To find:-

Find the value of k ?

Solution:-

Given points are A(2,6) and B(5,1)

Let (x1, y1)=A(2,6)=> x1 = 2 and y1 = 6

Let (x2, y2)=B(5,1)=>x2=5 and y2=1

Given ratio =2:3

Let m:n = 2:3=>m=2 and n=3

The Coordinates of a points which divides the linesegment joining the points A and B = C(k,4)

We know that

The Coordinates of a points which divides the linesegment joining the points A(x1, y1) and

B (x2, y2) in the ratio m:n is

[(mx2+nx1)/(m+n) , (my2+ny1)/(m+n)]

=>(k,4)=[(2×5+3×2)/(2+3) , (2×1+3×6)/(2+3)]

=>(k,4)=[(10+6)/5 , (2+18)/5]

=>(k,4)=(16/5,20/5)

=>(k,4)=(16/5,4)

On Comparing both sides then

=>k = 16/5

Answer:-

The value of k for the given problem is 16/5

Used formula:-

The Coordinates of a points which divides the linesegment joining the points A(x1, y1) and

B (x2, y2) in the ratio m:n is

[(mx2+nx1)/(m+n) , (my2+ny1)/(m+n)]