Final answer:
Homologous X chromosomes in female grasshoppers segregate during anaphase I of meiosis I, leading to the production of four haploid gametes with varied genetic combinations due to earlier crossovers.
Step-by-step explanation:
In the XX-XO sex determination system used by grasshoppers, the homologous X chromosomes segregate during meiosis I. Specifically, this segregation occurs during anaphase I when the homologous chromosomes are pulled to opposite poles of the cell. Following this, meiosis II resembles mitotic division, where the sister chromatids separate during anaphase II, resulting in four haploid gametes with varied genetic combinations due to crossover events that occurred earlier in prophase I. Importantly, these gametes contain a haploid set of chromosomes, which is essential for sexual reproduction and contributes to genetic diversity.