Here are the essential concepts you must grasp in order to answer the question correctly.
Distance Formula
The distance formula is used to calculate the distance between two points in a Cartesian plane. It is derived from the Pythagorean theorem and is expressed as d(P, Q) = √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of points P and Q, respectively. This formula allows for the determination of the straight-line distance between the two points.
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Midpoint Formula
The midpoint formula is used to find the coordinates of the midpoint M of a line segment connecting two points P and Q. It is given by M = ((x1 + x2)/2, (y1 + y2)/2), where (x1, y1) and (x2, y2) are the coordinates of points P and Q. This formula provides the average of the x-coordinates and the y-coordinates of the two points, resulting in the midpoint's coordinates.
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Coordinate System
A coordinate system is a two-dimensional plane defined by a horizontal axis (x-axis) and a vertical axis (y-axis). Each point in this system is represented by an ordered pair (x, y), indicating its position relative to the axes. Understanding the coordinate system is essential for applying the distance and midpoint formulas, as it allows for the visualization and calculation of geometric relationships between points.
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