Geometry

Question Analysis

The main focus is recognizing the figure as a rhombus (since the diagonals are perpendicular bisectors of each other) and using the formula  (where  and  are the lengths of the diagonals) to calculate its area. We need to find the lengths of the diagonals from the coordinates of the vertices.

Key Concept Explanation

For a rhombus, the area formula is , where  and  are the lengths of the two diagonals. The diagonals of a rhombus are perpendicular to 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  are  and of  are . Since they have the same  - coordinate, the length of  ( ) is .

2. Find the length of diagonal :

The coordinates of  are