Practice Analytic Geometry in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

Analytic geometry studies geometric objects using coordinate systems and algebraic equations.

It translates shapes into equations so algebra can solve geometry problems.

Example 1

medium
Prove that the triangle with vertices A(0,0), B(4,0), and C(2,2\sqrt{3}) is equilateral using coordinates.

Example 2

hard
Use coordinates to prove that the diagonals of a rectangle bisect each other.

Example 3

easy
Determine whether points P(1,2), Q(3,6), and R(5,10) are collinear using the slope method.

Example 4

medium
Show that quadrilateral A(1,1), B(4,2), C(5,5), D(2,4) is a parallelogram by comparing slopes of opposite sides.