Question 1

Write a program that outputs the equation of the perpendicular bisector of the line segment between two points. Your program should

prompt for and input the coordinates of two points [for example (2.0, 4.0) and (7.0, 2.0)];

compute the slope of the line between those two points;

compute the coordinates of the midpoint of the line segment between the two points by averaging the two x coordinates and the two y coordinates;

compute the slope of the perpendicular bisector by taking the negative reciprocal of the slope of the line segment;

compute the y intercept of the perpendicular bisector (you now have the slope m of the bisector and a point ( xmid , ymid ) on the bisector, so the y intercept is ymid m*xmid ); and

output the midpoint coordinates and the equation of the bisector as shown below.

The figure above illustrates the sample line segment mentioned above and its perpendicular bisector. Note: You need to consider the special cases where the perpendicular bisector is vertical or horizontal as shown in the sample runs 2 and 3.

Sample run 1 Enter x coordinate of point1: 2 Enter y coordinate of point1: -4 Enter x coordinate of point2: 7 Enter y coordinate of point2: -2 midpoint coordinates (4.50,-3.00) Bisector equation: y = -2.5 x +8.25

Sample run 2 Enter x coordinate of point1: 2.5 Enter y coordinate of point1: 10.5 Enter x coordinate of point2: 14.8 Enter y coordinate of point2: 10.5 midpoint coordinates (8.65,10.50) Bisector line is vertical with equation: x = 8.65

Sample run 3 Enter x coordinate of point1: 7.5 Enter y coordinate of point1: 3.8 Enter x coordinate of point2: 7.5 Enter y coordinate of point2: 20.5 midpoint coordinates (7.50,12.15) Bisector line is horizontal with equation: y = 12.15

In [ ]:

#%%writefile HW1Q1.py

# Your code for Question 1 in this cell

# After you finish writing your code and check that it is working correctly, 

# uncomment the first line and run your code so that it genrates HW1Q1.py file