Describe test cross. Why is it necessary?

(N/A) test cross is a genetic cross between an individual exhibiting a dominant phenotype (but with an unknown genotype) and an individual that is homozygous recessive for the trait.
It is necessary because,while genotypic ratios can be calculated using mathematical probability,it is not possible to determine the exact genotypic composition (homozygous dominant or heterozygous) simply by observing the phenotype of a dominant trait.
For example,it is impossible to distinguish between a tall plant with a $TT$ genotype and one with a $Tt$ genotype just by looking at it.
To solve this,Mendel devised the test cross.
$A$ back cross is defined as a cross of $F_{1}$ progeny back to one of their parents.
$A$ special type of back cross,where the $F_{1}$ progeny is crossed with the recessive parent,is known as a test cross.
This method allows us to determine if the dominant phenotype is homozygous or heterozygous.
For instance,in a monohybrid cross between a violet-flowered plant $(W)$ and a white-flowered plant $(w)$,the $F_{1}$ hybrid is a violet-flowered plant.
If all $F_{1}$ progeny are violet,the dominant parent is homozygous $(WW)$. If the progeny appear in a $1:1$ ratio of violet to white,the dominant parent is heterozygous $(Ww)$.
In the case of a dihybrid cross,such as a heterozygous violet and axial flower $(WwAa)$ crossed with a double recessive white and terminal flower $(wwaa)$,the resulting ratio will be $1:1:1:1$.