1. Let's start by understanding that coordinate geometry involves points, lines, and shapes in the coordinate plane. 2. A common problem is finding the distance between two points $A(x_1,y_1)$ and $B(x_2,y_2)$ using the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ 3. Another important formula is the midpoint formula, which finds the point exactly halfway between $A$ and $B$: $$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$ 4. For the equation of a line passing through two points, the slope $m$ is: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ 5. Then the line equation in point-slope form is: $$y - y_1 = m(x - x_1)$$ 6. These formulas help solve many coordinate geometry problems such as finding distances, midpoints, slopes, and equations of lines. 7. If you have a specific problem or example, please provide it, and I can guide you through the solution step-by-step.