19.16. Exercises

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.

   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))

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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)

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.

   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())

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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?

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)

   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)

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

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