Geometry

Question Analysis

The problem requires using coordinate plane metrics like distance and slope formulas to determine the properties of the quadrilateral formed by the given points, and then classify it accordingly.

Key Concept Explanation

Distance formula: is used to find side lengths. Equal side lengths suggest a rhombus or square.

Slope formula: helps find if sides are parallel (equal slopes) or perpendicular (negative reciprocal slopes).

Step-by-Step Solution

1. Calculate the distances between consecutive points:

Let , , ,

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