Final answer:
The distance and midpoint formulas in homework 3 are used for measuring distances and midpoints (Option C). These formulas help us calculate the straight-line distance and the exact center point between two coordinates, which are vital in various applications like physics and engineering.
Step-by-step explanation:
The distance and midpoint formulas referred to in homework 3 are used for measuring distances and midpoints between two points in a coordinate system. Option C) Measuring distances and midpoints is the correct purpose of these formulas. For example, the distance formula is derived from the Pythagorean theorem and is used to calculate the straight-line distance between two points on a plane. The midpoint formula, on the other hand, finds the middle point, or the average of two points' coordinates, which effectively gives you the exact center between them. These formulas are essential in geometry and are used in various applications such as physics for finding displacement or in engineering for determining the length of materials needed between two points.
To measure the average speed of an athlete, one needs to know the distance the athlete traveled and the time it took. In such scenarios, the distance can be calculated using the distance formula if the sprint is along a straight path or by using more complex methods if the path is curved. In contrast, the displacement only concerns the shortest path between the starting and ending points, which, for a straight sprint, is the same as the distance. Thus, understanding these measurements is crucial in different fields to describe motion and solve related problems.