# Draw a line between two points

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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.

Evan on 17 Jul 2013
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 on 17 Jul 2013
Actually I have an array like this:
[1 5.2
2 4.3
3 5.1
4 7.8
5 9.9
...];
I just want to show that we take only 2 points (1 and 5) and draw a line through them.
Evan on 17 Jul 2013
Ah, okay. I suppose you've been successful in modifying my below example code to be more in line with your needs?

Evan on 17 Jul 2013
Edited: Evan on 17 Jul 2013
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

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

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)
else
end