Find the ratio in which the point
P(4,24) divides the join of A(2,27) and
B( 10, 15)
Answers
Step-by-step explanation:
Given:-
The points are A(2,27) and B( 10, 15)
To find:-
Find the ratio in which the point P(4,24) divides
the line segment joining the points A(2,27) and
B( 10, 15) ?
Solution:-
Given points are A(2,27) and B( 10, 15)
Let (x1,y1)=A(2,27) => x1=2 and y1 = 27
Let (x2, y2)=B( 10, 15)=> x2=10 and y2=15
Let the required ratio = m1:m2
Dividing point P(x,y)=(4,24)
We know that
The coordinates of the point P(x,y) which divides the line segment joining the points A (x1, y1) and B(x2, y2) is
[(m1x2+ m2x1)/(m1+m2) , (m1y2+m2y1)/(m1+m2)]
On Substituting these values in the above formula then
=> P(4,24) =
[(m1×10+m2×2)/(m1+m2),(m1×15+m2×27)/(m1+m2)]
=> [(10m1+2m2)/(m1+m2) , (15m1+27m2)/(m1+m2)]
On Comparing both sides then
(10m1+2m2)/(m1+m2) = 4
=> 10 m1 + 2 m2 = 4(m1+m2)
=> 10 m1+2m2=4m1 + 4m2
=> 10m1 - 4m1 = 4m2-2m2
=> 6m1 = 2 m2
=> 6m1/2 = m2
=> m1/m2 = 2/6
=> m1/m2 = 1/3
=> m1:m2 = 1:3
(or)
(15m1+27m2)/(m1+m2) = 24
=> 15m1 +27m2 = 24(m1+m2)
=> 15m1+27m2 = 24m1+24m2
=> 27m2 -24m2 = 24m1 -15m1
=> 3m2 = 9m1
=> 3 /9 = m1/m2
=> 1/3 = m1/m2
=> m1/m2 = 1/3
=> m1:m2 = 1:3
Answer:-
The required ratio for the given problem is 1:3
Used formula:-
The coordinates of the point P(x,y) which divides the line segment joining the points A (x1, y1) and B(x2, y2) is
[(m1x2+ m2x1)/(m1+m2) , (m1y2+m2y1)/(m1+m2)]