We have found the coordinates of L as (2.5,-0.5). We can find M, the midpoint of BC, in the same way.
L
(x_1+x_2/2,y_1+y_2/2)
A&( 0, 0)
C&( 5, -1)
(0+ 5/2,0+( -1)/2)
L(2.5, -0.5)
M
(x_1+x_2/2,y_1+y_2/2)
B&( 2, 2)
C&( 5, -1)
(2+ 5/2,2+( -1)/2)
M(3.5, 0.5)
The coordinates of M are (3.5,0.5). Let's place the midpoints on the triangle and draw LM.
The slopes of the parallel lines are the same. Therefore, to verify that AB∥ML, we will use the Slope Formula to show that their slope are the same. Let's start with the slope of AB, m_1. Notice that the endpoints of AB are A( 0, 0) and B( 2, 2).
The slope of AB is 1. Using the same way, we can find the slope of ML, m_2.
m_1
m_1=y_2-y_1/x_2-x_1
A&( 0, 0)
B&( 2, 2)
m_1=2- 0/2- 0
m_1=1
m_2
m_2=y_2-y_1/x_2-x_1
M&( 3.5, 0.5)
L&( 2.5, -0.5)
m_2=-0.5- 0.5/2.5- 3.5
m_2=1
As a result, both AB and ML have the same slope, so they are parallel. Next, we will verify that LM= 12AB by finding AB and LM. Therefore, we will use the Distance Formula. Let's first find AB.
