Import math

class Point$2$D:

def $\_\_$init$\_\_($self$,$ x$,$ y$)$:

self.x $=$ x

self.y $=$ y

class Line:

def $\_\_$init$\_\_($self$,$ point$1,$ point$2)$:

self.p$1=$ point$1$

self.p$2=$ point$2$

pass

@property

def getDistance$($self$)$:

return round$($math$.$sqrt$($pow$($self$.$p$2.$x $-$ self.p$1.$x$,2)+$ pow$($self$.$p$2.$y $-$ self.p$1.$y$,2)),3)$

pass

@property

def getSlope$($self$)$:

if self.p$2.$x $-$ self.p$1.$x $==0$:

return math.inf

return round$(($self$.$p$2.$y $-$ self.p$1.$y$)/($self$.$p$2.$x $-$ self.p$1.$x$),3)$

pass

def $\_\_$str$\_\_($self$)$:

if self.p$2.$x $-$ self.p$1.$x $==0$:

return "Undefined"

elif self.getSlope $==0\mathrm{.}0$:

return f$"$y $=\{$round$($self$.$p$1.$y $-$ self.getSlope $*$ self.p$1.$x$,3)\}"$

return f$"$y $=\{$self$.$getSlope$\}$x $+\{$round$($self$.$p$1.$y $-$ self.getSlope$*$self$.$p$1.$x$,3)\}"$

$\_\_$repr$\_\_=\_\_$str$\_\_$

def $\_\_$mul$\_\_($self$,$other$)$:

#$---$ YOUR CODE CONTINUES HERE

def $\_\_$contains$\_\_($self$,$point$)$:

#$---$ YOUR CODE CONTINUES HERE

$\_\_$mul$\_\_$

A special method to support the $*$ operator. Returns a new Line object where the x$,$y attributes of every Point$2$D object is multiplied by an integer. The only operation allowed is Line$*$integer$,$ any other non$-$integer values return None.

$\_\_$contains$\_\_$

A special method to support the in operator. Returns True if the Point object lies on the Line object, False otherwise. You cannot make any assumptions about the value that will be on the right side of the operator. If the slope is undefined, return False.

Recall that floating$-$point numbers are stored in binary, as a result, the binary number may not accurately represent the original base $10$ number. For example:

$>>>0\mathrm{.}7+0\mathrm{.}2==0\mathrm{.}9$

False

This error, known as floating$-$point representation error, happens way more often than you might realize. To implement this method, you will need to compare floating$-$point numbers. Avoid checking for equality using $==$ with floats. Instead use the isclose$()$ method available in the math module:

$>>>$ import math

$>>>$ math.isclose$(0\mathrm{.}7+0\mathrm{.}2,0\mathrm{.}9)$

True

math.isclose$()$ checks if the first argument is acceptably close to the second argument by examining the distance between the first argument and the second argument, which is equivalent to the absolute value of the difference of the values:

$>>>$ x $=0\mathrm{.}7+0\mathrm{.}2$

$>>>$ y $=0\mathrm{.}9$

$>>>$ abs$($x$-$y$)$

$1\mathrm{.}1102230246251565$e$-16$

If abs$($x $-$ y$)$ is smaller than some percentage of the larger of x or y$,$ then x is considered sufficiently close to y to be "equal" to y$.$ This percentage is called relative tolerance.

Examples:

$>>>$ p$1=$ Point$2$D$(-7,-9)$

$>>>$ p$2=$ Point$2$D$(1,5\mathrm{.}6)$

$>>>$ line$1=$ Line$($p$1,$ p$2)$

$>>>$ line$2=$ line$1*4$

$>>>$ isinstance$($line$2,$ Line$)$

True $>>>$ line$2$ y $=1\mathrm{.}825$x $+15\mathrm{.}1$

$>>>$ line$3=$ line$1*4$

$>>>$ line$3$

y $=1\mathrm{.}825$x $+15\mathrm{.}1$

$>>>$ line$5=$Line$($Point$2$D$(6,48),$Point$2$D$(9,21))$

$>>>$ line$5$

y $=-9\mathrm{.}0$x $+102\mathrm{.}0$

$>>>$ Point$2$D$(45,3)$ in line$5$

False

$>>>$ Point$2$D$(34,-204)$ in line$5$

True

$>>>(9,5)$ in line$5$

False