Question

Determine a point which divides a line segment of length 12cm internally in the ratio of 2:3.Also, justify your construction.

Answer 1

Steps of Construction:

1. Draw a line segment AB of 12 cm

2. Through the points A and B draw two parallel line on the opposite side of AB

3. Cut 2 equal parts on AX and 3 equal parts on BY such that AX1=X1X2 and BX1=Y1Y2=Y2Y3.

4. Join X2Y3 which intersects AB at P∴APPB=23.

Justification:

In ΔAX2P and ΔBY3P, we have

∠APX2=∠BPY3 { Because they are vertically opposite angle}

∠X2AP=∠Y3BP { Because they are alternate interior angles }

ΔAX2P ΔBY3P { Because AA similarity }

∴ APBP=AX2BY3=23 { Because of C.P.C.T }

I hope it help you

Answer 2

Solution:



Steps of Construction:

1. Draw a line segment AB of 12 cm

2. Through the points A and B draw two parallel line on the opposite side of AB

3. Cut 2 equal parts on AX and 3 equal parts on BY such that AX1=X1X2 and BX1=Y1Y2=Y2Y3.

4. Join X2Y3 which intersects AB at P∴APPB=23.

Justification:

In ΔAX2P and ΔBY3P, we have

∠APX2=∠BPY3 { Because they are vertically opposite angle}

∠X2AP=∠Y3BP { Because they are alternate interior angles }

ΔAX2P ΔBY3P { Because AA similarity }

∴ APBP=AX2BY3=23 { Because of C.P.C.T }