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 Plane
The coordinate plane is a two-dimensional surface defined by a horizontal axis (x-axis) and a vertical axis (y-axis). Each point on the plane is represented by an ordered pair of numbers (x, y), indicating its position relative to the axes. Understanding the coordinate plane is essential for visualizing points, distances, and midpoints, as it provides the framework for geometric relationships in algebra.
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