How to plot 2 lines and find the coordinates of their intersection?

I need to plot the lines x+y=3 and x-y= -1 and find their point of intersection. I know that to plot the lines I could use 'fplot'. How can I find the coordinates of their intersection and plot it? Please help.

Answer 1

[Star Strider]

Another approach:

xymtx = [1   1; 1  -1];
cv = [3; -1];
xy = xymtx\cv;                                      % Calculate Intercept
xint = xy(2);                                       % X-Value Of Intercept
yint = xy(1);                                       % Y-Value Of Intercept

xyind = [xint - 1, xint + 1]';                      % X-Values For Plot
xydep = [cv -xyind.*xymtx(:,2)];                    % Y-Values For Plot

figure(1)
plot(xyind, xydep(1,:), xyind, xydep(2,:), '-r')
hold on
plot(xint, yint, 'pg', 'MarkerFaceColor','g', 'MarkerSize',10)
hold off

This is straightforward and relatively simple linear algebra. The ‘xydep’ variable calculates the y-values corresponding to the arbitrary values in ‘xydep’, and is the result of solving ‘[X + Y] = C’ for ‘Y’.

Answer 2

[Tutku Oztel]

Hello,

I'm sharing the function that I wrote to find the intersection points of two lines with their given slope and constant values:

function [x0 y0] = intersectPoints(m1,m2,b1,b2)
% Insersection point of two lines with known slope and constant
% parameters.
% [x0 y0] = intersectPoints(m1,m2,b1,b1)
% where m's are slope, and b's are constants.
% written by Tutku Öztel in 06.01.2019

x0 = (b2-b1)/(m1-m2); %find the x point
y0 = m1*x0+b1;
end

Late though, but still.. Hope it will be helpful! :)

Tutku

[José Luis Sandoval]

Usefuil, thanks.

[Wai Keong Bryce Wong]

This is super useful. Thanks for your help!

Answer 3

[Simon Kölbl]

I would do it like this:

% define x Axis and evaluate functions
x_points = -5:0.1:5;
function1 = -x+1;
function2 = x+1;
index_intersection = find(function1 == function2);
x_value_intersection = x_points(index_intersection);
y_value_intersection = function1(index_intersection);
% plot functions and intersection point:
curve1 = plot(x_points, function1);
hold on
curve2 = plot(x_points, function2);
intersection = plot(x_value_intersection, y_value_intersection,...
                'Marker', '+', 'MarkerSize', 6, 'Color', 'r');

[Cyril Okhio]

Sorry it did not work. There are errors in Line 9.

[Image Analyst]

@Cyril Okhio, I think @Simon Kölbl meant this:

clc;	% Clear command window.
fprintf('Running %s.m ...\n', mfilename);
clear;	% Delete all variables.
close all;	% Close all figure windows except those created by imtool.
workspace;	% Make sure the workspace panel is showing.

% Define x Axis and evaluate functions
x_points = -5:0.1:5;
function1 = -x_points+1;
function2 = x_points+1;
index_intersection = find(function1 == function2);
x_value_intersection = x_points(index_intersection)
y_value_intersection = function1(index_intersection)
% Plot functions and intersection point:
curve1 = plot(x_points, function1);
hold on
curve2 = plot(x_points, function2);
intersection = plot(x_value_intersection, y_value_intersection,...
	'Marker', '+', 'MarkerSize', 20, 'Color', 'r', 'LineWidth', 2);
grid on
caption = sprintf('At intersection, x = %f, y = %f', x_value_intersection, y_value_intersection);
fontSize = 15;
title(caption, 'FontSize', 15);
xlabel('x', 'FontSize', 15);
ylabel('y', 'FontSize', 15);
fprintf('Done running %s.m\n', mfilename);

Answer 4

[Matt J]

Using this File Exchange submission,

https://www.mathworks.com/matlabcentral/fileexchange/93470-intersections-of-multiple-2d-lines-or-line-segments

xy=linexlines2D( [1,1,-3].'  , [1,-1,1] ); %the intersection point

hold on
fimplicit(@(x,y)  x+y-3);
fimplicit(@(x,y)  x-y+1);
plot(xy(1),xy(2),'or','MarkerFaceColor','r')
hold off

Answer 5

[Preetham Manjunatha]

Here is the link to find the intersection point of two line segments/lines. A fast two line intersection point finder based on the line parametric space. Finds the intersection point between two lines if it exists or else submits NaN. if you need to find the intersection of the multiple line segments, MATLAB's Mapping Toolbox has function polyxpoly - that finds the intersection points for lines or polygon edges.