Let me first ask this :
how do u find the midnumber of 1 and 3 ?
( 1 + 3 ) Ă· 2 =
4 Ă· 2 =
2
It is the exact way we do to find the midpoint of a line ; have a look :
The midpoint of AB is P thus :
( Point A + Point B ) Ă· 2 = Point P
Suppose that we have point B as ( x , y ) then :
[ ( 2 , 3 ) + ( x , y ) ] Ă· 2 = ( 6 , - 1 )
Now we add the same components of points A and B together, that is, we add the first component A to the first component B and replace the first component, and so we add the second component A to the second component B. And replace the second component :
[ ( 2 + x , 3 + y ) ] Ă· 2 = ( 6 , - 1 )
( 2 + x/2 , 3 + y/2 ) = ( 6 , - 1 )
Well now we have a draw so the first components of both sides of the draw must be equal Also, the second components of the two sides of the equation must be equal , thus :
2 + x/2 = 6
Multiply both sides by 2
2 Ă— ( 2 + x )/2 = 2 Ă— 6
2 + x = 12
Subtract both sides 2
2 - 2 + x = 12 - 2
x = 10 &
3 + y/2 = - 1
Multiply both sides by 2
2 Ă— ( 3 + y )/2 = 2 Ă— ( - 1 )
3 + y = - 2
Subtract both sides 3
3 - 3 + y = - 2 - 3
y = - 5
And finally, after all the hardship and misery, we realized that
B = ( 10 , - 5 )
Which mean Option C is the correct answer.
And we're done...
