1. The problem is to understand the basics of coordinate geometry. 2. Coordinate geometry involves plotting points, lines, and shapes on the Cartesian plane using coordinates $(x, y)$. 3. The main formula for distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ which comes from the Pythagorean theorem. 4. The midpoint formula to find the point exactly halfway between two points is $$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$$. 5. The slope of a line through two points is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ which tells us how steep the line is. 6. The equation of a line can be written as $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 7. To plot points, you locate the $x$ coordinate on the horizontal axis and the $y$ coordinate on the vertical axis. 8. Understanding these basics allows you to solve many problems involving shapes, distances, and lines on the plane.