gen-define-coordinate-geometry-and-give-one-short-worked-example-0e19

Define coordinate geometry and give one short worked example.

# Coordinate Geometry **Coordinate geometry** (also called **analytic geometry**) is a branch of mathematics that uses algebraic equations and numerical coordinates to describe and analyze geometric shapes and their properties. It connects algebra and geometry by representing points, lines, curves, and shapes on a coordinate system (typically the Cartesian plane with x and y axes). ## Short Worked Example **Problem:** Find the distance between points A(1, 2) and B(4, 6). **Solution:** Using the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ Substituting the coordinates: $$d = \sqrt{(4 - 1)^2 + (6 - 2)^2}$$ $$d = \sqrt{3^2 + 4^2}$$ $$d = \sqrt{9 + 16}$$ $$d = \sqrt{25} = 5$$ **Answer:** The distance between points A and B is **5 units**.