Question

6. Using any one construction method, divide a line segment AB = 12 cm in the ratio 4 : 3.​

Answer 1

Answer:

Steps of construction: 1. Draw a line segment AB = 12 cm by using a ruler.

2. Through the points A and B draw two parallel line on the opposite side of AB and making the same acute angles with the line segment.

3. Cut 4 equal parts on AX and 3 equal parts on BY such that AX1 = X1 X2 X3 X4 and BY1 = Y1 Y2 Y3 Y4

4. Join X4 Y3 which intersects AB at P Hence,

$\frac{ap}{pb} = \frac{4}{3}$

Justification:

In ΔAX2 P and ΔBY3 P, we have

∠APX2 = ∠BPY3 [vertically opposite angle]

∠X2AP = ∠Y3BP [alternate interior angles]

ΔAX2 P ~ ΔBY3 P [Because AA similarity]

∴ $\frac{ap}{bp} = \frac{ax4}{by3} = \frac{4}{3}$ [From C.P.C.T]

Hope this answer helps you out.