II$.$ Enhancing a Triangle Class

Part A

In Desire$2$Learn you will find a $.$zip archive containing two Java classes: CartesianPoint.java and Triangle.java. Download and unzip that file. Compile both classes.

Part B

Add the following methods to the Triangle class:

public double getPerimeter$()-$ returns the perimeter of the triangle.

public boolean isEquilateral$()-$ returns true if the triangle is an equilateral triangle, false otherwise.

public boolean isRight$()-$ returns true if the triangle is a right$-$angle triangle, false otherwise. $($Hint: C an use the Pythagorean Formula$).$

Note: make use of methods in the CartesianPoint.java

Consult math texts or online sources if you forget the definitions of "equilateral" or "right$-$angle", or if you can't recall a formula.

IMPORTANT NOTE regarding equality comparisons$1$: When working with floating$-$point numbers in Java $($or any programming language$),$ calculations don't work out exactly as we might expect. For instance, we may perform some calculations and end up with an answer like: $3\mathrm{.}999999...$ instead of the expected answer of $4.$ This happens because of the limited precision used to store$/$represent floating$-$point numbers in a computer.

Therefore, rather than comparing two double values using:

you should instead calculate the difference between the two numbers and then compare that to some really, really small value. If the difference is less than that re ally small value, then the two numbers are, essentially, equal.

For example, use:

if $($Math$.$abs $($num$1-$num$2)$ TOLERANCE$)\{...$

where double TOLERANCE $=1E-14($or some other really small number$).$

Aside: Math.abs $($num$1-$num$2)$ simply gives the absolute value of the difference betwe n num$1$ and num$2.$

Continued on the next page...

${?}^1$ See also: Section $5\mathrm{.}3$ of the course textbook.

Part C

In a separate file, create a test driver that exercises the two new methods in your Triangle class; name this class TestTriangle. In your test driver, create at least $2$ Triangle objects $($one that is an equilateral triangle, and another that is a right triangle$).$ Call both methods on each of these objects and print out the results in a meaningful way, such as "The triangle t$2$ is not an equilateral triangle" or "The triangle t$2$ is a right$-$angle triange." Compile and run this program. Examine the output and return to part b if you notice any problems. Once it is running correctly, please save sample output.

Hint $($if you're having trouble coming up with test data$)$: For an equilateral triangle you can use the points ath.sqrt $\frac{3}{2},$ and for a right triangle you can use $(0\mathrm{.}0,0\mathrm{.}0),(1\mathrm{.}0,0\mathrm{.}0),(0\mathrm{.}0,1\mathrm{.}0).$

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This class represents a triangle shape using $3$ points.

@author Natalie Webber

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public class Triangle $\{$

private CartesianPoint pointA;

private CartesianPoint pointB;

private CartesianPoint pointC;

public Triangle $($double $x1,$ double $y1,$

double $x2,$ double y$2,$

double x$3,$ double y$3)\{$

point $A=$ new CartesianPoint $(x1,y1)$;

pointB $=$ new CartesianPoint $(x2,y2)$;

$\}$

pointC $=$ new CartesianPoint $(x3,y3)$;

public Triangle $($CartesianPoint p$1,$

CartesianPoint p$2,$

CartesianPoint p$3)\{$

pointA $=p1$;

pointB $=$ p$2$;

$\}$

pointC $=$ p$3$;

$\}$

public class CartesianPoint $\{$

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The $x$ value for the point.

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private double $x_i$

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The $y$ value for the point.

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private double $y$;

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Constructs a CartesianPoint object with the

given $x$ and $y$ values.

@param xVal the initial x value.

@param yVal the initial y value.

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public CartesianPoint $($double xVal, double yVal$)\{$

$x=$xVal;

$\}$

$y=$yVal;

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Calculates the distance between this

CartesianPoint and the specified one.

@param $2$ the $x$ value for the other point.

@param y$2$ the $y$ value for the other point.

@return the distance between the two points.

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public double distance $($double $x2,$ double y$2)\{$

double $dx=x-x2$;

double dy $=y-y2$;