Triangle ABC has vertices A(0,0), B(2,2), and C(5,-1). Find the coordinates of L, the midpoint of line segment AC, and M, the midpoint of line segment BC. Verify that line segment LM is parallel to line segment AB and LM= 1/2AB.
+128707 Midpoint of AC = [ (5 + 0) / 2 , (-1 + 00 / 2 ] = [5/2, -1/2] = L
Midpoint of BC = [ ( 2 + 5) / 2 , (-1 + 2) / 2 ] = [7/2, 1/2] = M
Slope of AB = [2 - 0] / [ 2 - 0] = 2/2 = 1
Slope of LM = [ -1/2 - 1/2] / [ 5/2 - 7/2] = [-1] / [ - 2/2] = -1 / 1 = 1
So....LM is parallel to AB
And the length of AB = sqrt(8) = 2sqrt(2)
And the length of LM = sqrt [ 7/2 - 5/2)^2 + ( 1/2 + 1/2)^2 ] = sqrt [ 1^2 + 1^2] = = sqrt(2) = (1/2)2sqrt(2)
