In visual studio code:

Problem $2$

Deliverable: problem$2$functions.h and problem$2$functions.cpp

$-$ Write a function named Distance that takes four double arguments for the x and y

coordinates of two points $($x$1,$ y$1,$ x$2,$ y$2),$ and returns the distance between those points

as a double. If the function is called with the coordinates of one point only, the second

point$$s coordinates should default to the origin $(0,0).$

Recall, the formula to compute the distance, d$,$ between two points is:

$=(21)$

$2$

$+(21)$

$2$

Example calls:

$-$ Distance$(3,4)$ should return $5($the distance between the point $(3,4)$ and

the point $(0,0)).$

$-$ Distance$(-1,3,11,-2)$ should return $13($the distance between the point

$(-1,3)$ and the point $(11,-2)).$

$-$ Write a function named OnCircle that takes the x and y coordinates of the center of a

circle as the first two parameters, the radius of the circle as the third parameter, and the

x and y coordinates of a point as the fourth and fifth parameters $($all doubles$).$ The

function should return $-1$ if the point lies inside of the circle, $0$ if the point lies on the

circle, and $1$ if the point lies outside of the circle.

Example calls:

$-$ OnCircle$(0,0,5,1,1)$ should return $-1$ because the point $(1,1)$ lies inside

the circle centered at $(0,0)$ with radius $5.$

$$

$-$ Write a function named OnLine that takes the x and y coordinates $($all doubles$)$ of three

points $($x$1,$ y$1,$ x$2,$ y$2,$ x$3,$ y$3).$ The function should return true if the three points lie on a

straight line, and false if they do not.

Example calls:

$-$ OnLine$(0,0,1,3,2,6)$ should return true because the three points $(0,0)$

$(1,3)$ and $(2,6)$ lie on a straight line

$-$ All three function prototypes should be included in problem$2$functions.h

$-$ All three functions should be implemented in problem$2$functions.cpp

$$

A makefile and some minimal unit tests have been included in problem$2$tests.zip.

To run the tests provided, create a directory containing only your problem$2$functions.h file, your problem$2$functions.cpp file, and the files extracted from the attached problem$2$tests.zip. Then type:

make testDistance

make testOnCircle

make testOnLine

Makefile: flags $=-$std$=$c$++17-$Wall $-$I $.$

$$

problem$2$functions.o : problem$2$functions.cpp problem$2$functions.h

$$ g$++$ $$($flags$)-$c $$<$

$$

testDistance : testDistance.cpp problem$2$functions.o

$$ g$++$ $$($flags$)$ $$^-$o $@

$./$$@

$$

testOnCircle : testOnCircle.cpp problem$2$functions.o

$$ g$++$ $$($flags$)$ $$^-$o $@

$./$$@

$$

testOnLine : testOnLine.cpp problem$2$functions.o

$$ g$++$ $$($flags$)$ $$^-$o $@

$./$$@

$$

clean :

$$ rm problem$2$functions.o testDistance testOnCircle testOnLine

$```$

$//$ limited tests for the OnCircle function

#include

using std::cout;

using std::endl;

#include"problem$2$functions.h$"$

int main$()\{$

if $($OnCircle$(0,0,3,-3,0)==0)$

cout $<<$ "Passed OnCircle$(0,0,3,-3,0)$ test" $<<$ endl;

else

cout $<<$ "Failed OnCircle$(0,0,3,-3,0)$ test" $<<$ endl;

if $($OnCircle$(0\mathrm{.}73,-5\mathrm{.}2,5,3\mathrm{.}73,-1\mathrm{.}2)==0)$

cout $<<$ "Passed OnCircle$(0\mathrm{.}73,-5\mathrm{.}2,5,3\mathrm{.}73,-1\mathrm{.}2)$ test" $<<$ endl;

else

cout $<<$ "Failed OnCircle$(0\mathrm{.}73,-5\mathrm{.}2,5,3\mathrm{.}73,-1\mathrm{.}2)$ test" $<<$ endl;

if $($OnCircle$(-8\mathrm{.}1,2\mathrm{.}7,13,4,7\mathrm{.}7)==1)$

cout $<<$ "Passed OnCircle$(-8\mathrm{.}1,2\mathrm{.}7,13,4,7\mathrm{.}7)$ test" $<<$ endl;

else

cout $<<$ "Failed OnCircle$(-8\mathrm{.}1,2\mathrm{.}7,13,4,7\mathrm{.}7)$ test" $<<$ endl;

if $($OnCircle$(-8\mathrm{.}1,2\mathrm{.}7,13,-20,7\mathrm{.}7)==-1)$

cout $<<$ "Passed OnCircle$(-8\mathrm{.}1,2\mathrm{.}7,13,-20,7\mathrm{.}7)$ test" $<<$ endl;

else

cout $<<$ "Failed OnCircle$(-8\mathrm{.}1,2\mathrm{.}7,13,-20,7\mathrm{.}7)$ test" $<<$ endl;

return $0$;

$\}$

$``````$

$//$ minimal tests of the Distance function

#include

using std::cout;

using std::endl;

#include"problem$2$functions.h$"$

int main$()\{$

if $($Distance$(3,4)==5)$

cout $<<$ "Passed Distance$(3,4)$ test" $<<$ endl;

else

cout $<<$ "Failed Distance$(3,4)$ test, function returned $"$

$<<$ Distance$(3,4)<<".$ Expected $5"<<$ endl;

if $($Distance$(0\mathrm{.}5,-1\mathrm{.}2,0\mathrm{.}5,1\mathrm{.}8)==3)$

cout $<<$ "Passed Distance$(1,-1,3,2)$ test" $<<$ endl;

else

cout $<<$ "Failed Distance$(0\mathrm{.}5,-1\mathrm{.}2,0\mathrm{.}5,1\mathrm{.}8)$ test, function returned $"$

$<<$ Distance$(0\mathrm{.}5,-1\mathrm{.}2,0\mathrm{.}5,1\mathrm{.}8)<<".$ Expected $3"<<$ endl;

if $($Distance$(-7\mathrm{.}1,2,-1,2)==6\mathrm{.}1)$

cout $<<$ "Passed Distance$(-7,2,-1,2)$ test" $<<$ endl;

else

cout $<<$ "Failed Distance$(-7\mathrm{.}1,2,-1,2)$ test, function returned $"$

$<<$ Distance$(-7\mathrm{.}1,2,-1,2)<<".$ Expected $6\mathrm{.}1"<<$ endl;

if $($Distance$(3,8,3,8)==0)$

cout $<<$ "Passed Distance$(3,8,3,8)$ test" $<<$ endl;

else

cout $<<$ "Failed Distance$(3,8,3,8)$ test, function returned $"$

$<<$ Distance$(3,8,3,8)<<".$ Expected $0"<<$ endl;

if $($Distance$(0\mathrm{.}5,2\mathrm{.}1,-11\mathrm{.}5,7\mathrm{.}1)==13)$

cout $<<$ "Passed Distance$(0\mathrm{.}5,2\mathrm{.}1,-11\mathrm{.}5,7\mathrm{.}1)$ test" $<<$ endl;

else

cout $<<$ "Failed Distance$(0\mathrm{.}5,2\mathrm{.}1,-11\mathrm{.}5,7\mathrm{.}1)$ test, function returned $"$

$<<$ Distance$(0\mathrm{.}5,2\mathrm{.}1,-11\mathrm{.}5,7\mathrm{.}1)<<".$ Expected