The mid point of a line segment is (6,_1) if one end point is (2,6) .Find the second end point
Answers
Answer:
16
Step-by-step explanation:
Step-by-step explanation:
Given:-
The mid point of a line segment is (6,_1) and one end point is (2,6) .
To find:-
Find the second end point?
Solution:-
Let the second end point of a line be (x2, y2)
One end point = (2,6)
Let (x1, y1)=(2,6)=>x1=2 and y2=6
The mid point of a linesegment joining the points (x1, y1) and (x2, y2) is denoted by M(x,y) and defined by
[(x1+x2)/2 , (y1+y2)/2]
=>M(x,y)=[(2+x2)/2 , (6+y2)/2]
According to the given problem
Mid point of the given linesegment = (6,-1)
=>[(2+x2)/2 , (6+y2)/2] = (6,-1)
On comparing both sides then
=>(2+x2)/2=6 and (6+y2)/2=-1
=>2+x2=6×2 and 6+y2=-1×2
=>2+x2=12 and 6+y2=-2
=>x2=12-2 and y2=-2-6
=>x2=10 and y2=-8
(x2, y2)=(10,-8)
The required point =(10,-8)
Answer:-
The second end point of the given line segment is (10,-8)
Check:-
We have (x1, y1)=(2,6)=>x1=2 and y2=6
(x2, y2)=(10,-8)=>x2=10 and y2=-8
Mid Point = [(x1+x2)/2 , (y1+y2)/2]
=>M(x,y)=[(2+10)/2 ,(6-8)/2]
=>M(x,y)=(12/2,-2/2)
M(x,y)=(6,-1)
Verified the given relation.
Used formula:-
The mid point of a linesegment joining the points (x1, y1) and (x2, y2) is denoted by M(x,y) and defined by
[(x1+x2)/2 , (y1+y2)/2]