Question

Find the length of AE if BD || AE and BD is a midsegment of ▲ACE

Answer 1

AC = 2 BD

Distance BD = √[(2.5+1)^2 +(3-3)^2]

Distance BD = √(3.5)^2

Distance BD = 3.5

AC = 2 * 3.5 = 7

Answer

d. 7

Answer 2

to the risk of sounding redundant.

well, in a triangle, the midsegment is half of its parallel base, namely in this case BD = ½AE.

well, what is the length of BD anyway?

well, we know its coordinates are -1,3 and 2.5,3

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ B(\stackrel{x_2}{2.5}~,~\stackrel{y_2}{3})\qquad D(\stackrel{x_1}{-1}~,~\stackrel{y_1}{3})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ BD=\sqrt{(-1-2.5)^2+(3-3)^2}\implies BD=\sqrt{(-3.5)^2+0^2} \\\\\\ BD=\sqrt{3.5^2}\implies BD=3.5\\\\ -------------------------------\\\\ BD=\cfrac{AE}{2}\implies 2BD=AE\implies 2(3.5)=AE\implies 7=AE$