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there are two lines form 3 point like so

Point 1 (1,2)

Point 2 (5,6)

Point 3 (7,1)

Lines are from

1 to 2

and from

1 to 3

what i need are the points on each line where the y (vertical) distance is at a given value (as an example 2)

from constracting this figure i've got on Line 1 to 2 an approximate Point (2.8,3.8) and on Line 1 to 3 an approximate Point (2.8,0.8)

is there a mathematically to solve this, I will need this for a given x value as well?

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Let the co-ordinates of two points be $A(x_1, y_1)$ and $B(x_2, y_2)$. The equation of the line AB is given by the “two point form”, which is:-

$\dfrac {y – y_1}{x – x_1} = \dfrac {y_2 – y_1}{x_2 – x_1}$; where (x, y) represents any particular point on that line.

That equation can somehow be reduced to a form say ax + by + c = 0; where a, b, c will be some numeric values.

If D(h, k) is a point on that line and is the point you are interested in (with the value of k known as given), then the value of h can be found by solving for h from the equation a(h) + b(k) + c = 0.

The process will be the same for finding n of E(m, n) if m is known.

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