How to find the location of a point on the line between other two points

geometry

When there are two point A and B, the location of their center point is $[(x_A + x_B)/2, (y_A + y_B)/2]$
$x_M, y_M$ is the coordinates of a point M.

How can I find the location of Point C located on A side than B.
This C is located between A and B.

For example, when the weight is 2:1, the distance between A and C is a half of the distance of B and C.

Best Answer

enter image description hereThe idea is similar. You need to use the concept of similar triangles. Suppose $A(x_1, y_1) $ and $B(x_2, y_2)$ are points. We want to find a point $C$ such that $AC: CB= m:n$. Then the coordinate of $C$ is given by

$$(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n}).$$

Observe that the red and the green triangles are similar since the corresponding angles of the triangles are equal. This implies that the ratio of their corresponding sides are equal. Therefore, $$\frac{x-x_1}{x_2-x} = \frac{m}{n}.$$ Now just solve for $x$. Use the exact same idea to find $y$. Does this help?

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