Question

Divide a line segment of length 14 cm internally in the ratio 2 : 5. Also, justify your construction.

Answer 1

Given that

Determine a point which divides a line segment of length 14cm internally in the ratio of 2:5.

We follow the following steps to construct the given

Step of construction

Step: I-First of all we draw a line segment AB = 14cm.

Step: II- We draw a ray AX making an acute angle ∠BAX = 60° with AB.

Step: III- Draw a ray BY parallel to AX by making an acute angle ∠ABY = ∠BAX.

Step IV- Mark of two points A₁, A₂ on AX and three points B₁, B₂, B₃, B₄, B₅ on BY in such a way that AAA1 = A1A2 = B1B2 = B₂B₃ = B₃B₄ = B₄B₅.

Step: V- Joins A₂B₃ and this line intersects AB at a point P.

Thus, P is the point dividing AB internally in the ratio of 2:5

Justification:-

In ΔAA₂P and ΔBB₅P we have

∠A₂AP = ∠PBB₅          [∠ABY = ∠BAX]

And ∠APA₂ = ∠BPB₅    [Vertically opposite angle]

So, AA similarity criterion, we have

ΔAA₂P ≈ ΔBB₅P

`(A A_2)/(BB_5)=(AP)(BP)`

`(AP)/(BP)=2/5`