Algebra and geometry are two important branches of mathematics, which are closely related in many aspects. Algebra mainly studies abstract concepts such as numbers, variables and equations, while geometry focuses on specific objects such as shape, size and position. Although their research objects and methods are different, we can combine algebra and geometry through some skills and methods, so as to better understand and solve mathematical problems.

First of all, we can relate geometric figures to algebraic equations through coordinate systems. For example, we can express the points on the plane in Cartesian coordinate system, and then describe the relationship between these points through algebraic equations. In this way, we can use algebraic methods to study the properties of geometric figures, such as distance and angle.

Secondly, we can use the concept of vector space to combine algebra with geometry. Vector space is a set of addition and scalar multiplication operations, which can represent vector, direction, length and other information in geometry. By studying the properties of vector space, we can better understand the transformation and motion law of geometric figures.

In addition, we can also use linear algebra to solve geometric problems. Linear algebra is a subject that studies linear relations and linear mappings in vector space, including concepts such as matrix, determinant, eigenvalue and eigenvector. Applying these concepts to geometric problems can simplify the process of solving problems and improve the efficiency of solving problems.