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Common Core (Vector and Matrix Quantities)

Common Core for Mathematics

Examples, solutions, videos, and lessons to help High School students learn to work with 2 × 2 matrices as a transformations of the plane, and interpret the absolute value of the determinant in terms of area.

Common Core: HSN-VM.C.12

The following diagram shows how to use determinants to find the area of a polygon. Scroll down the page for more examples and solutions.

**2D Area and determinants**

Introduction to calculating area of a parallelogram in the plane using a 2×2 determinant.

**Area of a triangle with determinants**

This method uses the formula of the parallelogram, by moving the triangle such that one vertex is at the origin.

**Determinants to Find the Area of a Triangle**

This video shows how to use determinants to find the area of a triangle where the vertices are not at the origin.

**Determinants to Find the Area of a Polygon**

This video shows how one can use determinants to find the area enclosed by any polygon.

**Application of Determinants: Area on the Coordinate Plane**

This video shows how to use determinants to calculate the area of a triangle and parallelogram on the coordinate plane.

The formula involves finding the determinant of a 3x3 matrix.

**Determinant of a matrix as the area scale factor of the transformation**

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