HSC Together Year 12 Maths Extension 1: Geometric Results of Vectors

Geometric Results of Vectors

This topic is part of the HSC Mathematics Extension 1 syllabus under the topic Vectors.

In this post, we will explore the geometric results of vectors. In particular, we will cover:

  • The diagonals of a parallelogram meet at right angles if and only if it is a rhombus
  • The midpoints of the sides of a quadrilateral join to form a parallelogram
  • The sum of the squares of the lengths of the diagonals of a parallelogram is equal to the sum of the squares of the lengths of the sides

 

Diagonal of a rhombus

The diagonals of a parallelogram meet at right angles if and only if it is a rhombus.

 

The midpoint of a parallelogram

The midpoints of the sides of a quadrilateral join to form a parallelogram.

 

Finally, the sum of the squares of the lengths of the diagonals of a parallelogram is equal to the sum of the squares of the lengths of the sides. This can be derived using the two theorems found above.

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