Refer to the following information to answer this question:

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

The horticulturalist has a red geranium with an uncertain genetic makeup. She crosses it with a white geranium ([tex]rr[/tex]) and gets a generation in which half of the plants have red flowers and half have white flowers. What does this combination of offspring tell her about the genetic makeup of the red geranium parent?

\[
\begin{array}{|c|c|c|}
\hline
& r & r \\
\hline
? & Rr & Rr \\
\hline
? & r & rr \\
\hline
\end{array}
\]

A. The red geranium is heterozygous for flower color ([tex]Rr[/tex]).

B. The red geranium is homozygous for red flowers ([tex]RR[/tex]).

C. The trait shows incomplete dominance.

D. The red geranium is homozygous for white flowers ([tex]rr[/tex]).

To determine the genetic makeup of the red geranium parent, let's examine the results of the cross between the red geranium and the white geranium, which is known to be homozygous recessive ([tex]rr[/tex]). The offspring result in half red-flowered plants and half white-flowered plants.

Step-by-Step Explanation:

**Understanding Alleles: **
- Red flowers are produced by the dominant allele [tex]R[/tex], thus the genotypes [tex]RR[/tex] (homozygous dominant) and [tex]Rr[/tex] (heterozygous) will produce red flowers.
- White flowers are produced by the recessive allele [tex]r[/tex], so only [tex]rr[/tex] (homozygous recessive) will result in white flowers.

**Cross Analysis: **
- The white geranium is [tex]rr[/tex], thus any allele it contributes is [tex]r[/tex].
- The progeny resulting are 50% red ([tex]Rr[/tex]) and 50% white ([tex]rr[/tex]).

**Infer the Red Parent's Genotype: **
- The only way to get a 50/50 distribution of red and white flowers is if the red parent is heterozygous ([tex]Rr[/tex]). This is because:
  - The [tex]Rr[/tex] plant crossed with [tex]rr[/tex] can produce offspring [tex]Rr[/tex] (red) and [tex]rr[/tex] (white) in equal proportions.

Therefore, the answer is A. The red geranium is heterozygous for flower color ([tex]Rr[/tex]).

By understanding the principles of Mendelian genetics and dominant/recessive inheritance, we can deduce the red geranium must have been heterozygous. This provides insight into how traits are inherited and helps the horticulturalist in her breeding goals.