Question

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

Answer 1

AE = 9 units

Step-by-step 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:

`D = \sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

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:

`BD = √((-1-3.5)^2+(1.5-1.5)^2)=4.5` 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 :)