Final answer:
Yes, you can obtain a pea plant variety that is homozygous for the tall trait with red fruit by using Mendelian genetics, crossing plants with the desired traits, and selecting for the traits over several generations.
Step-by-step explanation:
If you used two varieties of pea plants to start with, one being tall with red fruit and the other being dwarf with different colored fruit, by applying Mendelian genetics, you could indeed select for plants that are homozygous for the tall trait and red fruit.
Considering that tall (T) and red (R) are dominant traits, you would cross a homozygous recessive dwarf (tt) plant with one that is heterozygous (Tt) for the tall trait. Using a Punnett square to predict the offspring, the expected phenotypic ratio would be 1 tall for every 1 dwarf, suggesting that half of the F1 generation will exhibit the dominant tall trait, while the other half will be dwarf.
To achieve a generation of homozygous tall plants with red fruit, one would need to observe the results of crossing plants over several generations, selecting each time for those that exhibit both desired traits. Moreover, by crossing F1 plants among themselves or backcrossing with a parent, it is possible to increase the proportion of offspring that are homozygous dominant for the tall trait.
When analyzing offspring, if the observed phenotypic ratio aligns with the expected Mendelian ratios, like 3 tall to 1 dwarf, this would confirm that inheritance follows Mendelian principles. To ensure tall plants with red fruit are homozygous, further selection and breeding would be required to isolate the desired traits.