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
mediumProve that the triangle with vertices A(0,0), B(4,0), and C(2,2\sqrt{3}) is equilateral using coordinates.
Example 2
hardUse coordinates to prove that the diagonals of a rectangle bisect each other.
Example 3
easyDetermine whether points P(1,2), Q(3,6), and R(5,10) are collinear using the slope method.
Example 4
mediumShow that quadrilateral A(1,1), B(4,2), C(5,5), D(2,4) is a parallelogram by comparing slopes of opposite sides.