Asked by Artyom
on 17 Jul 2013

Hi. I have three points [5.2 0 0 0 9.9 0 0 12.1]. How to draw a line through the first two points and find is the third point (12.1) above/below this line.

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Answer by Evan
on 17 Jul 2013

Edited by Evan
on 17 Jul 2013

Accepted answer

P = [1 5.2; 2 0; 3 0; 4 0; 5 9.9; 6 0; 7 0; 8 12.1]; posP = find(P(:,2)); %find where y values aren't zero. C = polyfit(P(posP(1:2),1),P(posP(1:2),2),1); %fit line to first and second nonzero Y = polyval(C,P(posP(3),1)); %find value on line at x-value of third nonzero

if Y == P(posP(3),2) disp('The third point falls on the line') elseif Y > P(posP(3),1) disp('The third point falls above the line') elseif Y < P(posP(3),1) disp('The third point falls below the line') end

Answer by Iain
on 17 Jul 2013

This is the raw maths...

point1 = [x1 y1]; point2 = [x2 y2]; point3 = [x3 y3];

m = (y2 - y1) / (x2 - x1); c = y2 - m*x2;

y3_est = m*x3 + c; if y3_est > y3 disp('point below line') elseif y3_est == y3 disp('colinear') else disp('point above line') end

Answer by Kiran Sagar
on 17 Jul 2013

Frame an equation between two of the points of the form y=mx+c. then replace x with the x-cordinate of the point to be checked, compare the resultant y with the point's y cordinate. that's it. supposing your two points forming the line are the first and last rows of the matrix A, and the test point as one of the in between points, here is a probable code:

A = [1 5.2; 2 0; 3 0; 4 0; 5 9.9;]; m = (A(5,2)-A(1,2))/(A(5,1)-A(1,1)); c = A(1,2)-m*A(1,1); y_test = m*A(2,1)+c; if y_test<A(2,2) %%%%% your statements %%%%% else %%%%%your statements%%% end

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## 5 Comments

## Evan (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/82369#comment_160283

How are your points arranged in the vector you provide? Is this a 3d line? Are they arranged [x1 y1 z1 x2 y2 z2...]?

## Artyom (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/82369#comment_160289

They are arranged like this:

## Evan (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/82369#comment_160303

Okay. You say you have three points, but your array seems to contain eight. Are you saying you only want to consider points where your y value is not zero? That is, you would plot a line through (1,5.2) and (5,9.9) then see if (9,12.1) is above or below the line?

I'll go ahead and submit a solution under this assumption. If I'm mistaken, just let me know any I'll modify it as needed.

## Artyom (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/82369#comment_160310

Actually I have an array like this:

I just want to show that we take only 2 points (1 and 5) and draw a line through them.

## Evan (view profile)

Direct link to this comment:http://www.mathworks.com/matlabcentral/answers/82369#comment_160334

Ah, okay. I suppose you've been successful in modifying my below example code to be more in line with your needs?