find the length of AE if BD AE and BD is a midsegment of ACE

Accepted Solution

Answer:AE = 9 unitsExplanation:We know that the line joining two midpoints in a triangle is parallel to the third side and equals half its lengthIn the diagram, we are given that:segment BD // segment AE and that segment BD is a mid-segment of the ΔACEAccording the above theorem, we can conclude that:BD = 0.5 × AE ......................> I1- getting the length of BD:Length of segment BD can be calculated using the distance formula:[tex]D = \sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]We are given that:B is at (3.5,1.5) which means that x₁ = 3.5 and y₁=1.5D is at (-1,1.5) which means that x₂=-1 and y₂=1.5Substitute in the formula:[tex]BD = \sqrt{(-1-3.5)^2+(1.5-1.5)^2}=4.5[/tex] units2- getting the length of AE:using equation I:BD = 0.5 × AE4.5 = 0.5 × AEAE = 2 × 4.5AE = 9 unitsHope this helps :)