Question $2$: $k-$Nearest neighbours

Table $1$ is a modified subset of a dataset used to classify flowers.

Table $1$: length and width used to classify items

A new instance new is found, and has to be classified.

$($a$)$ Plot all $11$ data points in Table $1,$ using length and width as the axes, to show

their relative positions to the new instance.

$($b$)$ Use the $k-$NN algorithm with the Euclidian distance measure and $k=3.$

Calculate the distances between new and the existing data points. Show all

the calculated distances on your plot of the data points. Indicate the $k$ closest

neighbours clearly, and show the resulting classification.

Show ALL your calculations.

$($c$)$ Is $k=3$ the correct value of $k$ to use for the dataset in Table $1?$ Explain why

or why not, and how to find the optimal value for $k.$