Connecting Algebra and Geometry

Analytic geometry blends algebraic equations with geometric shapes, letting you describe lines, circles, parabolas, and more using coordinates and formulas.

Equations of Common Shapes

• Line: \( y = mx + b \)
• Circle: \( (x - h)^2 + (y - k)^2 = r^2 \)
• Parabola: \( y = ax^2 + bx + c \)

Distance and Midpoint

• Distance: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \)
• Midpoint: \( M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \)

Practical Uses

From GPS navigation to video game graphics, analytic geometry makes it possible to model and analyze locations and paths in the real world.