Question

3. Find the midsegment of triangle BCD, which is parallel to BC. Label the endpoints of the midsegment as E and G.

What are the coordinates of E and G? ________________

Show work verifying that EG and BC are parallel.______________

Answer 1

Since we want the midsegment that's parallel to BC, the endpoints will be the
midpoints of BD and CD. So
Midpoint BD:
((-3 + -1)/2, (1 + -3)/2) = (-4/2, -2/2) = (-2,-1)
Midpoint CD:
((3+ -1)/2, (3 + -3)/2) = (2/2, 0/2) = (1, 0)
So the coordinates of E & G are (-2,-1) and(1,0) respectively.
Segment EG will be parallel to segment BC if they have the same slope. So
Slope BC:
(3 - 1)/(3 - -3) = 2/6 = 1/3
Slope EG
(0 - -1)/(1 - -2) = 1/3
Since both EG and BC have the same slope, they are parallel.