Dividing line segments

The  exercise appears under the Geometry Math Mission. This exercise abstracts the idea of midpoint to a point that cuts a segment into a particular ratio.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the coordinates of the point in the middle: This problem provides a segment and specifies that it has to be cut in a certain ratio. The student is asked to find the correct coordinates of the point that cuts the segment as desired.Dls1.png
 * 2) Find the coordinates of the endpoint: This problem provides an endpoint and a middle point that splits a segment into a certain ratio. The student is asked to find the other endpoint.Dls2.png

Strategies
Knowledge of the midpoint formula can help start the understanding that is needed for this exercise, but an ability to work with ratios is all that is necessary.
 * 1) To ensure accuracy, calculate the distance and then set up the ratios using distance formula.
 * 2) Similar triangles can be used to increase efficiency.
 * 3) The numbers involved work "nicely" with the ratios given.
 * 4) Simplifying the ratio so that one of the arguments is one can assist accuracy and efficiency.

Real-life Applications

 * 1) Distance and an ability to calculate a portion of the way is important for mapping and cartography. Techniques like this, along with trigonometry, were used to find the heights of mountains before satellite technology.