Certainly! Let's tackle this genetics question using Mendelian principles.
The problem states that the offspring of a particular cross are 100% heterozygous for the trait of plant height. We are provided with four potential pairs of parent genotypes, and we need to determine which pair is most likely to have produced these heterozygous offspring.
### Step-by-Step Solution:
1. Heterozygous Offspring (Tt):
- If all offspring are heterozygous (Tt), each offspring receives one dominant allele (T) and one recessive allele (t) from its parents.
2. Analyze Possible Parent Genotypes:
- Let's analyze each provided option to determine which could lead to 100% heterozygous offspring:
a. [tex]$Tt' \times tt$[/tex]:
- Here, [tex]$Tt'$[/tex] (where T is dominant and t' indicates another allele) and tt (homozygous recessive).
- The cross would yield:
- T from [tex]$Tt'$[/tex] and t from tt → Tt (heterozygous)
- t' from [tex]$Tt'$[/tex] and t from tt → t't (not necessarily heterozygous in traditional terms, but for understanding let's denote as mixed genotype).
b. [tex]$Tt \times Tt$[/tex]:
- Both parents are heterozygous.
- The offspring could be TT, Tt, Tt, tt (in a 1:2:1 ratio), but not 100% heterozygous. This option doesn't meet the 100% heterozygous condition.
c. [tex]$tt \cdot t$[/tex]:
- This notation appears to be a typo as it doesn't represent a valid genotype for plant height traits.
d. [tex]$TT \times tt$[/tex]:
- One parent is homozygous dominant (TT) and the other is homozygous recessive (tt).
- All offspring would receive a T from TT and a t from tt, resulting in 100% Tt (heterozygous).
3. Conclusion:
- The only pair of parent genotypes that guarantees 100% heterozygous offspring (Tt) is the pairing of [tex]$TT$[/tex] (homozygous dominant) and [tex]$tt$[/tex] (homozygous recessive).
Therefore, the most likely genotypes of the parents are:
[tex]\[ TT \times tt \][/tex]
Given this analysis, we see that the correct and most likely answer is:
[tex]\[ \boxed{TT \cdot tt} \][/tex]
