Triangle abc has vertices a(0,0), b(2,2) and c(5,-1). find the coordinates of l, the midpoint of line ac, and m, the midpoint of line bc. verify that line lm is parallel to line ab, and line lm is half of line ab.

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 .