Prove using slope of lines that line segment joining the midpoint of $\overline { AB}$ and $\overline{AC}$ in $\Delta ABC$ is parallel to $\overline {BC.}$
Need to prove using slope of lines means I can prove slope of both the lines are equal, So they are parallel.
But here i don't know how to assume coordinates of all the points.
By locating your coordinate axes with origin at B and the x-axis pointing along BC, you can assume that B has coordinates (0,0) and C had coordinates (c,0) for some c and A has coordinates (a,h) for some a and h.
Then the midpoint of BA is (a/2, h/2) and the midpoint of CA is ( (a+c)/2, h/2 ). The line joining these two points then has slope zero, which is the same as the slope of BC.