Connecting Algebra and Geometry

Analytical geometry, also called coordinate geometry, uses algebraic equations to describe geometric shapes. By placing points, lines, and curves on a coordinate plane, we can analyze and solve geometric problems using equations.

Common Objects

• Lines: Described by equations like \( y = mx + b \).
• Circles: Defined by \( (x - h)^2 + (y - k)^2 = r^2 \), where \( (h, k) \) is the center and \( r \) is the radius.
• Parabolas: Graphed as \( y = ax^2 + bx + c \).

Why It’s Useful

Analytical geometry lets us calculate distances, midpoints, and slopes—tools essential for engineering, design, and navigation.