Answer:
AE = 9 units
Explanation:
We know that the line joining two midpoints in a triangle is parallel to the third side and equals half its length
In the diagram, we are given that:
segment BD // segment AE and that segment BD is a mid-segment of the ΔACE
According the above theorem, we can conclude that:
BD = 0.5 × AE ......................> I
1- 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=1.5
D is at (-1,1.5) which means that x₂=-1 and y₂=1.5
Substitute in the formula:
[tex]BD = \sqrt{(-1-3.5)^2+(1.5-1.5)^2}=4.5[/tex] units
2- getting the length of AE:
using equation I:
BD = 0.5 × AE
4.5 = 0.5 × AE
AE = 2 × 4.5
AE = 9 units
Hope this helps :)
