Math Problem Statement

Use coordinate geometry to verify which of the figures may be classified as a rhombus.

Solution

To determine which of these figures can be classified as a rhombus, we need to analyze their geometric properties using their coordinates. A rhombus is a quadrilateral where all four sides are equal in length.

Here’s the step-by-step process to verify the figures:

  1. Extract the vertices from each figure.
  2. Calculate the lengths of all sides using the distance formula: Distance between two points (x1,y1) and (x2,y2)=(x2x1)2+(y2y1)2\text{Distance between two points } (x_1, y_1) \text{ and } (x_2, y_2) = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
  3. Confirm if all four sides are equal for each figure.

Would you like me to analyze the coordinates for each figure and verify?

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Math Problem Analysis

Mathematical Concepts

Coordinate Geometry
Properties of a Rhombus

Formulas

Distance formula: √((x2 - x1)^2 + (y2 - y1)^2)

Theorems

A rhombus is a quadrilateral with all sides of equal length

Suitable Grade Level

Grades 8-10