Question

State and prove the section formula of external division
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Answer 1

Section formula for external division:

`P(x,y)=((mx_2+nx_1)/(m+n) ,(my_2+ny_1)/(m+n) )`

By drawing two comparable right triangles, the evidence for this result is similar to the proof for internal divisions.

What is section formula?

If we know the ratio of the internal distances of any two points from the provided location, we may use the section formula to obtain the coordinates of that point.

If we were to determine the coordinates of the point P, we might use the formula below by knowing the coordinates of the points A and B and the ratio of their distances to the provided point P. (section formula).

Since all other values must be provided, any formula with two or more variables can be used to determine the value of any variable. Therefore, the formula also include the other quantities.

Another well-known coordinate geometry formula exists and is a specific instance of the section formula.

If a point is equally spaced from the provided points, the mid-point formula may be used to get its coordinates. (where the ratio of m to n is 1:1)

Thanks,

Eddie