Expressing Geometric Properties with Equations
PrintExpressing Geometric Properties with Equations uses coordinates to prove geometric theorems and derive equations of conic sections. Circle equations are derived from the Pythagorean theorem, and parabola equations are derived from the focus-directrix definition. Slope, distance, and midpoint formulas serve as tools for proving properties of triangles, quadrilaterals, and polygons in the coordinate plane.
Example Problems
The equation of a circle is given below.
What is its center?
What is its center?
The parabola is reflected across the -axis.
What is the equation of the new parabola?
What is the equation of the new parabola?
What are the foci of the hyperbola represented by the equation
?
?
Triangle ABC has the following vertices:
A
B
C
Is triangle ABC a right triangle?
A
B
C
Is triangle ABC a right triangle?
Write the equation of a line that is parallel to and that passes through the point .

1-on-1 AI tutoring aligned to G-GPE. Instant help for students, real-time insights for teachers.
Used in classrooms by 100,000+ students at Baltimore County, Plano ISD, Deer Valley USD, KIPP, and districts nationwide.
Free for teachers, forever →