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

def getDistance$($self$)$:

#$---$ YOUR CODE CONTINUES HERE

def getSlope$($self$)$:

#$---$ YOUR CODE CONTINUES HERE

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

#$---$ YOUR CODE CONTINUES HERE

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

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

#$---$ YOUR CODE CONTINUES HERE

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

#$---$ YOUR CODE CONTINUES HERE

The Line class represents a $2$D line that stores two Point$2$D objects and provides the distance between the two points and the slope of the line using the property methods getDistance and getSlope. The constructor of the Point$2$D class has been provided in the starter code. You might use the math module

getDistance$($self$)$

A property method that gets the distance between the two Point$2$D objects that created the Line. The formula to calculate the distance between two points in a two$-$dimensional space is:

Returns a float rounded to $3$ decimals. To round you can use the round method as round$($value$,$

#ofDigits$)$

getSlope$($self$)$

A property method that gets the slope $($gradient$)$ of the Line object. The formula to calculate the slope using two points in a two$-$dimensional space is:

If the slope exists, returns a float rounded to $3$ decimals, otherwise, returns infinity as a float $($inf float$).$ To round you can use the round method as round$($value$,$ #ofDigits$)$

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$1.$getDistance

$16\mathrm{.}648$

$>>>$ line$1.$getSlope

$1\mathrm{.}825$

$\_\_$str$\_\_($self$)$ and $\_\_$repr$\_\_($self$)$

Special methods that provide a legible representation for instances of the Line class. Objects will be represented using the "slope$-$intercept" equation of the line: y $=$ mx $+$ b

To find b$,$ substitute m with the slope and y and x for any of the points and solve for b$.$ b must be rounded to $3$ decimals.. To round you can use the round method as round$($value$,$ #ofDigits$).$ The representation will be the string $$Undefined$$ if the slope of the line is undefined. You are allowed to define a property method to compute the interception b$.$ Note that the representation must account for all ranges of values for m and b: y $=$ b when x $=0,$ y $=$ mx $$ b when b is negative, etc.

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$1$

y $=1\mathrm{.}825$x $+3\mathrm{.}775$

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

$>>>$ line$5$

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

$>>>$ line$6=$Line$($Point$2$D$(2,6),$ Point$2$D$(2,3))$

$>>>$ line$6.$getDistance

$3\mathrm{.}0$

$>>>$ line$6.$getSlope inf $>>>$ line$6$

Undefined

$>>>$ line$7=$Line$($Point$2$D$(6,5),$ Point$2$D$(9,5))$

$>>>$ line$7$ y $=5\mathrm{.}0$

$\_\_$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.

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