Write a proof for the sectional formula?
Step 1. Draw the figure on a coordinate plane that divides the line segment internally in the ratio
Consider the point on a coordinate plane.
Step 2. Determine the coordinate :
From the figure, observe the following:
Since , by AA similarity:
The coordinates of are as follows:
From :
Step 3. Determine the coordinate :
From :
Step 4: Determine the section formula :
Hence, the point on a coordinate plane that divides the line segment internally in the ratio is .