Section 19.17 Exercises

Activity 19.17.1.

Add a distanceFromPoint method that works similar to distanceFromOrigin except that it takes a Point as a parameter and computes the distance between that point and self.

Solution.

import math

class Point:
    """ Point class for representing and manipulating x,y coordinates. """

    def __init__(self, initX, initY):
        """ Create a new point at the given coordinates. """
        self.x = initX
        self.y = initY

    def getX(self):
        return self.x

    def getY(self):
        return self.y

    def distanceFromOrigin(self):
        return ((self.x ** 2) + (self.y ** 2)) ** 0.5

    def distanceFromPoint(self, otherP):
        dx = (otherP.getX() - self.x)
        dy = (otherP.getY() - self.y)
        return math.sqrt(dy**2 + dx**2)

p = Point(3, 3)
q = Point(6, 7)
print(p.distanceFromPoint(q))

Activity 19.17.2.

Add a method reflect_x to Point which returns a new Point, one which is the reflection of the point about the x-axis. For example, Point(3, 5).reflect_x() is (3, -5)

Activity 19.17.3.

Add a method slope_from_origin which returns the slope of the line joining the origin to the point. For example,

>>> Point(4, 10).slope_from_origin()
2.5

What cases will cause your method to fail? Return None when it happens.

Solution.

class Point:
    """ Point class for representing and manipulating x,y coordinates. """

    def __init__(self, initX, initY):
        """ Create a new point at the given coordinates. """
        self.x = initX
        self.y = initY

    def getX(self):
        return self.x

    def getY(self):
        return self.y

    def distanceFromOrigin(self):
        return ((self.x ** 2) + (self.y ** 2)) ** 0.5

    def slope_from_origin(self):
        if self.x == 0:
           return None
        else:
           return self.y / self.x


p = Point(4, 10)
print(p.slope_from_origin())

Activity 19.17.4.

The equation of a straight line is “y = ax + b”, (or perhaps “y = mx + c”). The coefficients a and b completely describe the line. Write a method in the Point class so that if a point instance is given another point, it will compute the equation of the straight line joining the two points. It must return the two coefficients as a tuple of two values. For example,

>>> print(Point(4, 11).get_line_to(Point(6, 15)))
>>> (2, 3)

This tells us that the equation of the line joining the two points is “y = 2x + 3”. When will your method fail?

Activity 19.17.5.

Add a method called move that will take two parameters, call them dx and dy. The method will cause the point to move in the x and y direction the number of units given. (Hint: you will change the values of the state of the point)

Solution.

class Point:
    """ Point class for representing and manipulating x,y coordinates. """

    def __init__(self, initX, initY):
        """ Create a new point at the given coordinates. """
        self.x = initX
        self.y = initY

    def getX(self):
        return self.x

    def getY(self):
        return self.y

    def distanceFromOrigin(self):
        return ((self.x ** 2) + (self.y ** 2)) ** 0.5

    def move(self, dx, dy):
        self.x = self.x + dx
        self.y = self.y + dy

    def __str__(self):
        return str(self.x) + "," + str(self.y)


p = Point(7, 6)
print(p)
p.move(5, 10)
print(p)

Activity 19.17.6.

Given three points that fall on the circumference of a circle, find the center and radius of the circle.

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