find the ratio in which the line segment joining (-3,10) (6,8) is divided by (k,2). also find the k
Answers
Step-by-step explanation:
Given :-
The points (-3,10) and (6,8)
To find :-
1) Find the ratio in which the line segment joining (-3,10) (6,8) is divided by (k,2).
2)Find the value of k ?
Solution :-
Given points are (-3,10) and (6,8)
Let (x1, y1) = (-3,10)=>x1 = -3 and y1 = 10
Let (x2, y2)=(6,8) => x2 = 6 and y2 = 8
The point which divides the line segment joining the given points = (k,2)
Let the required ratio be (m1,m2)
We know that
The coordinates of the point which divides the linesegment joining the points (x1, y1) and ( x2,y2) in the ratio m1:m2 is
( { m1x2+m2x1}/(m1+m2) , {m1y2+m2y1}/(m1+m2) )
=> ( { m1(6)+m2(-3)}/(m1+m2) , {m1(8)+m2(10)}/(m1+m2) ) = (k,2)
( {6m1-3m2}/(m1+m2) , {8m1+10m2}/(m1+m2)) = (k,2)
On comparing both sides then
=> (6m1-3m2}/(m1+m2) = k ------------(1)
and
(8m1+10m2}/(m1+m2) = 2
=> 8m1 + 10m2 = 2( m1+m2)
=> 8m1 + 10 m2 = 2m1 + 2m2
=> 8m1 -2m1 = 2m2 - 10m2
=> 6m1 = -8m2
=>m1/m2 = -8/6
=> m1/m2 = -4/3
m1:m2 = -4:3
Let m1 = -4x and m2 = 3x then
On Substituting these values in (1) then
(6m1-3m2}/(m1+m2) = k
=>k =[ 6(-4x)-3(3x)]/(-4x+3x)
=> k =[-24x-9x)/(-x)
=> k = -33x/-x
=> k = 33
k = 33
Answer:-
The required ratio for the given problem is -4:3
The Value of k for the given problem is 33
Used formulae:-
Section formula:-
The coordinates of the point which divides the linesegment joining the points (x1, y1) and ( x2,y2) in the ratio m1:m2 is
( { m1x2+m2x1}/(m1+m2) , {m1y2+m2y1}/(m1+m2) )