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Swati Umamaheshwaran on 17 Sep 2017

Answered: Preetham Manjunatha on 8 Feb 2022

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.

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### Answers (5)

Star Strider on 17 Sep 2017

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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’.

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Tutku Oztel on 9 Jan 2019

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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

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José Luis Sandoval on 7 Jun 2020

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https://www.mathworks.com/matlabcentral/answers/357026-how-to-plot-2-lines-and-find-the-coordinates-of-their-intersection#comment_887846

Usefuil, thanks.

Wai Keong Bryce Wong on 12 Oct 2020

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https://www.mathworks.com/matlabcentral/answers/357026-how-to-plot-2-lines-and-find-the-coordinates-of-their-intersection#comment_1052126

This is super useful. Thanks for your help!

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Simon Kölbl on 17 Sep 2017

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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');

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Cyril Okhio on 13 Nov 2018

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https://www.mathworks.com/matlabcentral/answers/357026-how-to-plot-2-lines-and-find-the-coordinates-of-their-intersection#comment_636946

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

Image Analyst on 5 Jun 2021

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https://www.mathworks.com/matlabcentral/answers/357026-how-to-plot-2-lines-and-find-the-coordinates-of-their-intersection#comment_1565965

Open in MATLAB Online

@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);

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Matt J on 5 Jun 2021

Edited: Matt J on 5 Jun 2021

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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

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Preetham Manjunatha on 8 Feb 2022

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.

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