Hover over each shape for tool tips with color information

For this program you will be writing code that simulates throwing a dart randomly at the painting. To do this, you can repeatedly generate a random coordinate within the painting area and test to see which shape $($if any$)$ the dart falls into. Note that the two$-$dimensional plane is $800$ units wide $\backslash$times $500$ units high and origin point $(0,0)$ is at the top left corner, so you will be generating coordinates within this range as part of your simulation. When you are finished you should calculate the $\%$ chance of a dart hitting a particular shape.

Refer to the diagram below for the exact measurements of the painting and locations of shapes. As you$$re getting started, simulate just one dart toss and use the coordinate plane to determine if the dart has fallen into one of the colored regions. Begin with the red rectangle since it will be the simplest shape to work with$$how can you write a statement to determine if a point falls within a rectangle?

From there, expand this logic and apply it to the other shapes. Hint: you can use the distance formula from assignment $3$ again to determine if a point falls within a circular region. Once you are confident that you$$ve designed an effective algorithm, you can scale up and place your code inside a count$-$controlled loop.

Here are two examples of the program running followed by some additional tips.

How many dart throws? $10000$

Green: $1,296(12\mathrm{.}96\%)$

Yellow: $1,695(16\mathrm{.}95\%)$

Red: $1,010(10\mathrm{.}10\%)$

Gray: $623(6\mathrm{.}23\%)$

Blue: $657(6\mathrm{.}57\%)$

Black: $107(1\mathrm{.}07\%)$

Miss: $4,612(46\mathrm{.}12\%)$

How many dart throws? $-1000$

Please enter a positive number: $0$

Please enter a positive number: $50000$

Green: $6,277(12\mathrm{.}55\%)$

Yellow: $8,845(17\mathrm{.}69\%)$

Red: $5,064(10\mathrm{.}13\%)$

Gray: $3,388(6\mathrm{.}78\%)$

Blue: $3,432(6\mathrm{.}86\%)$

Black: $570(1\mathrm{.}14\%)$

Miss: $22,424(44\mathrm{.}85\%)$

This simulation approximates a solution to a problem; because of this, you will see different numbers when you run your program. The percentages that are generated should roughly match the percentages shown here. The more dart throws you compute the closer you will get to the actual solution.

You can generate a random floating point number within a given range by using the random module$$s uniform$()$ function. This function takes two arguments$$a low boundary and a high boundary$$and generates a floating point number within this range $($edges inclusive$).$

The coordinate system shown here is one that is standard in the world of computer graphics. Notice that the origin point $(0,0)$ is at the top left corner of the plane and that the x and y axes involve positive values.

You will need to validate input $($to ensure your program works with positive numbers$)$ and format the output with commas for thousands and two decimal places for percentages.

$8_{}$