Find the point of coordinate which divides the line segment joining the points (4, -3) and (-4,-6) into three equal parts
Answers
Step-by-step explanation:
Given:-
the points (4, -3) and (-4,-6)
To find:-
Find the point of coordinate which divides the line segment joining the points (4, -3) and (-4,-6) into three equal parts .
Solution:-
The points divides the linesegment are called Trisectional points or Points of trisection .
The Trisectional points divides the given linesegment in the ratio 1:2 or 2:1
Let The points which divides the given linesegment are P and Q
Coordinates of P:-
Let (x1, y1)=(4,-3)=>x1= 4 and y1 = -3
(x2, y2)=(-4,-6)=>x2 = -4 and y2 = -6
The ratio = m1:m2 = 1:2 =>m1 = 1 and m2 = 2
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)}]
On Substituting the values then
=>P(x,y)=[{1(-4)+2(4)}/(1+2) ,{1(-6)+2(-3)}/(1+2)]
=>P(x,y)=[(-4+8)/3,(-6-6)/3]
=>P(x,y)=(4/3,-12/3)
P(x,y)=(4/3,-4)
Coordinates of Q:-
Let (x1, y1)=(4,-3)=>x1= 4 and y1 = -3
(x2, y2)=(-4,-6)=>x2 = -4 and y2 = -6
The ratio = m1:m2 = 2:1 =>m1 = 2 and m2 = 1
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)}]
On Substituting the values then
=>Q(x,y)=[{2(-4)+1(4)}/(2+1) ,{2(-6)+1(-3)}/(2+1)]
=>Q(x,y)=[(-8+4)/3 ,(-12-3)/3]
=>Q(x,y)=(-4/3,-15/3)
Q(x,y)=(-4/3 , -5)
Answer:-
The coordinates of the points which divides the linesegment joining the given points are (4/3,-4) and (-4/3,-5)
Used formulae:-
Trisectional points:-
- The points divides the linesegment are called Trisectional points or Points of trisection .
- The Trisectional points divides the given linesegment in the ratio 1:2 or 2:1
- 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)}]
Answer:
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