Find a point on a segment between two points knowing only one coordinate I have two points for which I know both $x$ and $y$, and another point, which is on the line between the two previous points for which, knowing its $x$, I would like to know its $y$.
What's the formula? I tried to search online but it seems to be a too basic question.
 A: Let the known points be$A(x_1,y_1)$  and $B(x_2,y_2)$
Let the unknown point be$C(x,y)$
As ABC forms a straight line, different segments have equal slopes. So the formula is,
$$\frac{y_2 - y_1}{x_2 -x_1} = \frac{y - y_1}{x -x_1}$$
Plug in the known values and you'll find y.
A: Welcome. Any point$a, (x_a, y_a)$ on a line $l$ satisfies this relation:
$m= \frac{y_a-y_b}{x_a-x_b}$
where  m is gradient of line and $b, (x_b, y_b)$ is any arbitrary point on line $l$.So find m from points you have, then plug x in above relation and find y.
A: 
For a segment of a particular line, the ratio of its projection to the $y$-axis to its projection to the $x$-axis is constant.
For the segment $\overline {AB}$ the ratio is $${ y_{_B}-y_{_A} \over x_{_B}-x_{_A}},$$
for the segment $\overline {AC}$ the ratio is $${ y-y_{_A} \over x-x_{_A}}$$
So we obtain
\begin{align}
{ y-y_{_A} \over x-x_{_A}} &= { y_{_B}-y_{_A} \over x_{_B}-x_{_A}} \\[1em]
\end{align}
and from it
\begin{align}
{ y-y_{_A}} &= { y_{_B}-y_{_A} \over x_{_B}-x_{_A}}\cdot  (x-x_{_A}) \\[1em]
 \color{red} {y} &\color{red}= \color{red}{{ y_{_B}-y_{_A} \over x_{_B}-x_{_A}}\cdot  (x-x_{_A}) + y_{_A}}
\end{align}
