The vertices of a quadrilateral are A(-5,-2) B(-2,5)...

The vertices of a quadrilateral are $A(-5,-2) B(-2,5)$ $C(2,-2),$ and $D(-1,-9) .$ Determine whether each segment is a side or a diagonal of the quadrilateral, and find the slope of each segment.
$$\overline{B D}$$

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Key Concepts

Coordinate Geometry

Coordinate geometry, also known as analytic geometry, involves using the coordinate plane to represent geometric figures and solve geometric problems by algebraic means. This approach allows one to use coordinates to compute distances, slopes, and to distinguish between different types of segments such as sides and diagonals in polygons.

Slope

Slope is a measure of the steepness or incline of a line, calculated as the ratio of the change in the vertical direction (rise) to the change in the horizontal direction (run) between any two points on the line. It is crucial in determining the direction of a segment and for comparing the orientation of different segments in the coordinate plane.

Sides vs. Diagonals

In the context of polygons such as quadrilaterals, a side is a segment that connects two consecutive vertices, whereas a diagonal connects two non-consecutive vertices. Distinguishing between sides and diagonals is important for understanding the geometry of the figure and for calculating properties like slopes, lengths, or angles relevant to the structure of the polygon.

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