Geometry

Question Analysis

The main focus is recognizing the figure as a rhombus and using the formula  (where  and  are the lengths of the diagonals) to calculate its area. We need to determine the lengths of the diagonals from the given coordinates of the vertices.

Key Concept Explanation

For a rhombus, the area is calculated using the formula . The diagonals of a rhombus are perpendicular bisectors of each other, and this formula is derived from dividing the rhombus into four right - angled triangles.

Step - by - Step Solution

1. Find the length of diagonal :

The coordinates of  and  have the same  - coordinate. The length of  ( ) is .

2. Find the length of diagonal :

The coordinates of

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