Prompt the user to enter $3$ points on a standard Cartesian coordinate plane. You can assume the user will enter these values as floating$-$point numbers.

Compute the distance between each points$$you will be computing $3$ distance values. The distance formula is below. Note that you can raise a value to the $0\mathrm{.}5$ power to compute the square root, or you can use the sqrt$()$ function in the math module $-$ your choice!

$(($x$1-$x$2)^2+($y$1-$y$2)^2)^0\mathrm{.}5$

Report the distance to the user of each side, rounded to $2$ decimal places

Next, determine if the three points could form a valid triangle. You can assume that the triangle is valid by checking the following. Note that ALL THREE of these conditions must be met in order for a triangle to be valid:

$-$Side $1+$ Side $2$ must be longer than Side $3$

$-$Side $2+$ Side $3$ must be longer than Side $1$

$-$Side $3+$ Side $1$ must be longer than Side $2$

If the triangle is valid, report whether it is an equilateral, isosceles, or scalene triangle:

$-$Equilateral Triangle: all sides of the triangle have the same length

$-$Isosceles Triangle: only two sides of the triangle have the same length

$-$Scalene Triangle: all sides of the triangle have different lengths

Hint: when comparing the size of each triangle it may be helpful to compare a $$rounded$$ version of the length of each side. Due to floating point inaccuracies you may run into a where two values are virtually identical but Python will evaluate them to be different $($i$.$e$.0\mathrm{.}000000001!=0\mathrm{.}0).$ You can use the round$()$ function. The round function takes in two arguments, the value you want rounded, and the amount of decimal places to round to$.$ For example, round$(3\mathrm{.}14159,2)->3\mathrm{.}14.$

Extra Credit: Also report if the triangle is a right triangle $($i$.$e$.$ it has one angle of $90$ degrees$).$ You can do this by using the Pythagorean Theorem $($ a$2+$ b$2=$ c$2)$ on the sides of the triangle

Hint: $$c$($the hypotenuse$)$ MUST be the largest side for the Pythagorean Theorem to work. Use an $$if$$ statement to find the largest side and then test to see if the theorem holds.

Hint #$2$: round your numbers to $0$ decimal points for the purpose of this calculation. For example, round$($a$2)+$ round$($b$2)==$ round$($c$2)$

Sample Runs: $($Check graph for sample$)$

valid and invalid triangles

Enter Point #$1-$ x position: $0$

Enter Point #$1-$ y position: $0$

Enter Point #$2-$ x position: $50$

Enter Point #$2-$ y position: $86\mathrm{.}6$

Enter Point #$3-$ x position: $100$

Enter Point #$3-$ y position: $0$

The length of each side of your test shape is:

Side $1$: $100\mathrm{.}00$

Side $2$: $100\mathrm{.}00$

Side $3$: $100\mathrm{.}00$

This is a valid triangle!

This is an equilateral triangle

Enter Point #$1-$ x position: $0$

Enter Point #$1-$ y position: $0$

Enter Point #$2-$ x position: $0$

Enter Point #$2-$ y position: $100$

Enter Point #$3-$ x position: $100$

Enter Point #$3-$ y position: $0$

The length of each side of your test shape is:

Side $1$: $100\mathrm{.}00$

Side $2$: $100\mathrm{.}00$

Side $3$: $141\mathrm{.}42$

This is a valid triangle!

This is an isosceles triangle.

This is also a right triangle.

Enter Point #$1-$ x position: $110$

Enter Point #$1-$ y position: $100$

Enter Point #$2-$ x position: $75$

Enter Point #$2-$ y position: $25$

Enter Point #$3-$ x position: $0$

Enter Point #$3-$ y position: $0$

The length of each side of your test shape is:

Side $1$: $82\mathrm{.}76$

Side $2$: $148\mathrm{.}66$

Side $3$: $79\mathrm{.}06$

This is a valid triangle!

This is a scalene triangle

Enter Point #$1-$ x position: $0$

Enter Point #$1-$ y position: $0$

Enter Point #$2-$ x position: $50$

Enter Point #$2-$ y position: $50$

Enter Point #$3-$ x position: $100$

Enter Point #$3-$ y position: $100$

The length of each side of your test shape is:

Side $1$: $70\mathrm{.}71$

Side $2$: $141\mathrm{.}42$

Side $3$: $70\mathrm{.}71$

This is not a valid triangle

Ensure that your program is well$-$commented, and that comments serve to document the logical flow of the program.