Answer:
The coordinates of L are :(5/2,-1/2)
The coordinates of M are :(7/2,1/2)
Hence , LM is parallel to AB since the midpoint theorem states that the line joining the midpoints of any two sides of a triangle is parallel to the third side and is half or 1/2 of the third side
Step-by-step explanation:
We know ,
Midpoint of line xy=(x1+x2)/2 , (y1+y2)/2
" " " "AC=(0+5)/2 , (0+(-1))/2
=5/2 , -1/2
Again,
Midpoint of BC= (2+5)/2 , (2+(-1))/2
" " " " = 7/2 , 1/2
Now ,
Since L and M are the midpoints of AC and BC respectively , the line formed by them i.e. LM is the line that connects the midpoints of any two sides of a triangle and according to the midpoint theorem of triangle , the line joining the two midpoints is parallel to the third side and half its length .