Points P and Q are on line segment AB, and both points are on the same side of the midpoint M of AB. Point P divides AB in the ratio 2:3 and Q divides AB in the ratio 3:4. If PQ = 2, then what is the length of AB?

AP = (AB) and AQ = (AB).

< so the positions as shown above are correct.

(AB) – (AB) = 2

→ 35 · ( (AB) – (AB)) = 35 · 2

→ 5 · 3(AB) – 7 · 2(AB) = 35 · 2

→ 15(AB) – 14(AB) = 70

→ AB = 70.

→ 5 · 3(AB) – 7 · 2(AB) = 35 · 2

→ 15(AB) – 14(AB) = 70

→ AB = 70.