COORDINATE GEOMETRY Given each set of vertices, determine whether □E F G H is a rhombus, a recta

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COORDINATE GEOMETRY Given each set of vertices, determine...

COORDINATE GEOMETRY Given each set of vertices, determine whether $\square E F G H$ is a rhombus, a rectangle, or a square. List all that apply. Explain your reasoning.
$$E(-7,3), F(-2,3), G(1,7), H(-4,7)$$

Key Concepts

Quadrilateral Classification

Quadrilateral classification involves analyzing the properties of four-sided figures, such as side lengths, angles, and parallelism of opposite sides. This systematic approach helps distinguish between different types of quadrilaterals like rectangles, rhombuses, and squares.

Slope Formula

The slope formula determines the steepness or inclination of a line segment connecting two points in the Cartesian plane. This concept is essential for checking whether sides are parallel or perpendicular, which helps in identifying right angles and verifying properties of rectangles and squares.

Properties of Rhombus, Rectangle, and Square

Each quadrilateral type has defining characteristics: a rhombus has four congruent sides but does not necessarily have right angles; a rectangle has equal opposite sides with four right angles; a square meets both criteria by having equal sides and four right angles. Understanding these properties allows one to determine the nature of a quadrilateral by verifying its side lengths and angles.

Coordinate Geometry

Coordinate geometry provides a framework for representing geometric figures using algebraic equations. It allows one to analyze geometric properties by plotting points in the plane and using formulas to find distances, slopes, and other relationships between these points.

Distance Formula

The distance formula is derived from the Pythagorean theorem and is used to calculate the distance between any two points in the coordinate plane. This formula is critical when determining whether a quadrilateral has equal side lengths or when comparing the lengths of sides to classify shapes.

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