In the coordinate plane, we can learn important things about shapes by looking at their equations and coordinates. Here are some basic properties to know:

1. Lines:

   • Lines can be written as equations like $y = mx + b$.
   • Here, $m$ shows how steep the line is and the direction it goes.
   • The $b$ is where the line crosses the y-axis.

2. Triangles:

   • To find the area of a triangle, you can use this formula:
     $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
   • You can also find the area using the Shoelace method with the points where the corners are located.

3. Circles:

   • The equation for a circle looks like this: $(x - h)^2 + (y - k)^2 = r^2$.
   • In this formula, $(h, k)$ is the center of the circle, and $r$ is how far out from the center it goes.
   • The distance from the center to any point on the edge of the circle is always the same.

4. Rectangles and Squares:

   • Rectangles have opposite sides that are equal in length and parallel.
   • To find the area of a rectangle, use this formula: $A = l \times w$.
   • For squares, the area can be calculated with $A = s^2$, where $l$ is the length, $w$ is the width, and $s$ is the length of one side.

Knowing these properties can help you graph shapes and solve geometry problems better.