(5) Complete the following activity.
Find the ratio in which point T(-1, 6) divides the line segment joining the
points S(-3, 10) and R(6,-8).
By section formula,
mx, + NX
m +n
mo Itnx
+
..-1 =
m +n
1
X =
..-m -N =
... -m - 6m = -3n+n
..-7m = -2n
m
n
59
Answers
Step-by-step explanation:
Given:-
Given points are : S(-3, 10) and R(6,-8).
To find:-
Find the ratio in which point T(-1, 6) divides the line segment joining the points S(-3, 10) and R(6,-8).
Solution:-
Given points are :S(-3, 10) and R(6,-8).
Let (x1, y1)=(-3,10)=>x1 = -3 and y1 = 10
Let (x2, y2)=(6,-8)=>x2 = 6 and y2 = -8
And The given point which divides the linesegment joining the points S and R = T(-1,6)
Let the ratio be m:n
We know that
The Point P which divides the linesegment joining the points internally in the ratio m:n is
P(x,y)=[(mx2+nx1)/(m+n) ,(my2+ny1)/(m+n)]
T(-1,6)=[{(m)(6)+(n)(-3)}/(m+n), {(m)(-8)+(n)(10)}/(m+n)]
=>(-1,6)=[(6m-3n)/(m+n) , (-8m+10n)/(m+n)]
On comparing both sides then
=>-1 = (6m-3n)/(m+n)
=>6m-3n =-1( m+n)
=>6m -3n = -m-n
=>6m +m = -n+3n
=>7m = 2n
=>m/n = 2/7
=>m:n = 2:7
(or)
(-8m+10n)/(m+n) =6
=>-8m+10n = 6(m+n)
=>-8m +10n = 6m +6n
=>-8m-6m = 6n-10n
=>-14m = -4n
=>m/n= -4/-14
=>m/n = 4/14
=>m/n = 2/7
=>m:n = 2:7
Answer:-
The required ratio for the given problem is 2:7
Used formulae:-
Section formula:-
The Point P which divides the linesegment joining the points internally in the ratio m:n is
P(x,y)=[(mx2+nx1)/(m+n) ,(my2+ny1)/(m+n)]