determine a line perpendicular to the other line going through a certain point by python

Question

step1. I do linear regression for a bunch of points and get a line. step2. I get a center point by averaging this bunch of point step3. I want to find a line perpendicular to the regression line in step1 and going through the center point mentioned in step2.

what I thought: suppose the regression line y1=k1*x1+b1, the perpendicular line y2 = k2*x2+b2, then, k2 = -1/k1

Question: from the graph, looks like the two straight lines are not perpendicular.why? what happened

my python code: `

import numpy as np
import scipy.linalg
import matplotlib.pyplot as plt
from openpyxl import load_workbook


x = [140.0, 139.0, 145.0, 151.0, 156.0, 160.0, 162.0, 162.0, 156.0, 139.0, 129.0, 124.0, 125.0, 128.0, 127.0, 126.0, 126.0, 132.0, 139.0, 145.0, 150.0, 156.0, 155.0, 148.0, 135.0, 129.0, 125.0, 127.0, 128.0, 126.0, 123.0, 124.0, 130.0, 135.0, 142.0, 151.0, 158.0, 155.0, 148.0, 140.0, 126.0, 124.0, 127.0, 127.0, 126.0, 126.0, 126.0, 131.0, 138.0, 141.0, 159.0, 167.0, 162.0, 155.0, 147.0, 141.0, 138.0, 140.0, 140.0, 140.0, 138.0, 143.0, 150.0, 155.0, 163.0, 173.0, 178.0, 173.0]
y  = [621.0, 621.0, 630.0, 638.0, 636.0, 635.0, 635.0, 634.0, 628.0, 623.0, 617.0, 614.0, 618.0, 622.0, 617.0, 610.0, 612.0, 622.0, 626.0, 623.0, 622.0, 624.0, 625.0, 618.0, 613.0, 607.0, 608.0, 614.0, 614.0, 608.0, 603.0, 612.0, 616.0, 617.0, 616.0, 618.0, 622.0, 622.0, 615.0, 609.0, 607.0, 610.0, 612.0, 607.0, 606.0, 601.0, 611.0, 617.0, 615.0, 614.0, 619.0, 624.0, 625.0, 619.0, 615.0, 613.0, 618.0, 622.0, 616.0, 610.0, 614.0, 628.0, 625.0, 624.0, 628.0, 638.0, 646.0, 645.0]

def get_center(x,y):
    x = x[:-1]
    y = y[:-1]
    x0 = np.mean(x)
    y0 = np.mean(y)
    return x0, y0

#center point
x0,y0 = get_center(x,y)

#linear regression 
# fit_fn is now a function which takes in x and returns an estimate for y
fit = np.polyfit(x,y,1)
fit_fn = np.poly1d(fit) 

plt.plot(x0,y0,'bo')
#get the linear regression line
plt.plot(x,y, 'ro', x, fit_fn(x), '--k')

#get the perpendicular line going through the center point
plt.plot(x,(-1.0/fit[0])*(x-x0)+y0,'--b')
plt.grid(True)
plt.show()

this is the link of the graph I got by running the program

`

Answer 1

Because the x and y axis do not have the same scale

Add the line plt.axis([120, 180, 590, 650]) for example, to have both the x axis and the y axis display the same amount of labels (60)