High School

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------------------------------------------------ A horticulturist wants to produce geraniums with specific characteristics. She knows that the trait of red flowers is governed by the allele [tex]$R (RR$[/tex] and [tex]$Rr)$[/tex] and the trait of white flowers is governed by the allele [tex]$r (rr)$[/tex].

The horticulturist plans to cross a geranium that is true-breeding for red flowers with a geranium that is true-breeding for white flowers. Which Punnett square best describes that cross?

A.
[tex]\[

\begin{array}{|c|c|c|}

\hline

& R & r \\

\hline

R & RR & Rr \\

\hline

r & Rr & \pi \\

\hline

\end{array}

\][/tex]

B.
[tex]\[

\begin{array}{|c|c|c|}

\hline

& r & r \\

\hline

R & Rr & Rr \\

\hline

r & rr & rr \\

\hline

\end{array}

\][/tex]

C.
[tex]\[

\begin{array}{|c|c|c|}

\hline

& r & r \\

\hline

R & Rr & Rr \\

\hline

R & Rr & Rr \\

\hline

\end{array}

\][/tex]

Answer :

Certainly! Let's work through the cross of the geraniums using a Punnett square.

### Problem Understanding:

1. Traits and Alleles:
- Red flowers are governed by the allele [tex]\( R \)[/tex]. Red flowers occur when the genotype is either [tex]\( RR \)[/tex] or [tex]\( Rr \)[/tex].
- White flowers are governed by the allele [tex]\( r \)[/tex]. White flowers occur only when the genotype is [tex]\( rr \)[/tex].

2. Cross Information:
- A geranium that is true-breeding for red flowers will have the genotype [tex]\( RR \)[/tex].
- A geranium that is true-breeding for white flowers will have the genotype [tex]\( rr \)[/tex].

### Setting Up the Punnett Square:

- Parent Genotypes:
- One parent is [tex]\( RR \)[/tex] (red flowers).
- The other parent is [tex]\( rr \)[/tex] (white flowers).

To find out the possible genotypes of the offspring when these two plants are crossed, we can use a Punnett square.

### Completing the Punnett Square:

1. Labeling the square:
- On the top of the square, place the alleles from one parent.
- On the side of the square, place the alleles from the other parent.

Since one parent is [tex]\( RR \)[/tex] and the other is [tex]\( rr \)[/tex], it will look like this:
[tex]\[
\begin{array}{c|c|c}
& R & R \\
\hline
r & & \\
\hline
r & & \\
\end{array}
\][/tex]

2. Filling in the possible offspring genotypes:

- The first intersection (top left): [tex]\( R \)[/tex] from the top mating with [tex]\( r \)[/tex] from the side results in [tex]\( Rr \)[/tex].
- The top right: [tex]\( R \)[/tex] from the top mating with [tex]\( r \)[/tex] from the side results in another [tex]\( Rr \)[/tex].
- The bottom left: [tex]\( R \)[/tex] from the top mating with [tex]\( r \)[/tex] from the side results again in [tex]\( Rr \)[/tex].
- The bottom right: [tex]\( R \)[/tex] from the top mating with [tex]\( r \)[/tex] from the side results in [tex]\( Rr \)[/tex].

The completed Punnett square looks like this:
[tex]\[
\begin{array}{c|c|c}
& R & R \\
\hline
r & Rr & Rr \\
\hline
r & Rr & Rr \\
\end{array}
\][/tex]

### Conclusion

- Offspring Genotypes:
- All of the offspring will be [tex]\( Rr \)[/tex], which means they all will have red flowers, as the presence of a single [tex]\( R \)[/tex] allele is enough for the flowers to be red.

Therefore, the correct Punnett square that describes this genetic cross is option C.