Question

Help me i this please

the segment joining the midpoint of 2 sides f a triagle is parallel to the 3rd side and half as long.

thaks

Answer 1

let A be at (0,0)
Then if B is at (xb,yb), the length of AB is √(xb^2 + yb^2)

Then, if C is at (xc,yc), the midpoint of AC is (xc/2,yc/2) and the midpoint of BC is at ((xb+xc)/2,(yb+yc)/2)

If M is the midpoint of AC and N is the midpoint of BC, then the slope of MN is
((yb+yc)/2-yc/2)/((xb+xc)/2-xc/2) = (yb/2)/(xb/2) = yb/xb which is the slope of AB. So, MN || AB.

I'll leave it to you to show that MN is half of AB in length.