Why the plant have taproot have reticulate venation and the plant have fibrous root have parallel venation

Your friend is right. However, I would like to elaborate her answer. 

Tap roots and fibrous roots have different water absorbing capacities. Fibrous roots form a dense network of roots in the top soil and they absorb water from the top soil. While tap roots are long and thick with a greater surface area and they reach the deeper layers of soil. So, they are more efficient in water absorption from deeper layers. So, plants with tap root needs more water for their growth and development. While plants with fibrous roots do not need much water.