Question

Two line segments AB and AC include an angle of 60° where AB = 5 cm and AC = 7 cm. Locate points P and Q on AB and AC, respectively such that AP = `3/4` AB and AQ = `1/4` AC. Join P and Q and measure the length PQ.

Answer 1

Steps of construction:

1. Draw a line segment AB = 5 cm.
2. Draw ∠BAZ = 60°.
3. With centre A and radius 7 cm, draw an arc cutting the line AZ at C.
4. Draw a ray AX, making an acute ∠BAX.
5. Divide AX into four equal parts, namely AA₁ = A₁A₂ = A₂A₃ = A₃A₄.
6. Join A₄B.
7. Draw A₃P || A₄B meeting AB at P.
8. Hence, we obtain, P is the point on AB such that AP = `3/4` AB.
9. Next, draw a ray AY, such that it makes an acute ∠CAY.
10. Divide AY into four parts, namely AB₁ = B₁B₂ = B₂B₃ = B₃B₄.
11. Join B₄C.
12. Draw B₁Q || B₄C meeting AC at Q. We get, Q is the point on AC such that AQ = `1/4` AC.
13. Join PQ and measure it.
14. PQ = 3.25 cm.