Coordinate Geometry is a branch of mathematics that deals with geometric figures using coordinate systems. It plays a crucial role in various fields such as engineering, physics, computer science, and many more. By using coordinates, we can represent geometric shapes, equations, and solve complex problems efficiently.

To find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane, we use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
This formula is derived from the Pythagorean theorem and helps us calculate the shortest distance between two points on a plane.

The Section Formula is used to find the coordinates of a point that divides a line segment into a given ratio. If a line segment AB is divided by a point P(x, y) in the ratio m:n, then the coordinates of point P can be calculated using the formula:
x = ((mx2 + nx1)/(m + n)), y = ((my2 + ny1)/(m + n))
This formula is very useful in dividing line segments and determining the coordinates of the dividing point.

The slope of a line is a measure of its steepness or inclination. It tells us how much the line rises or falls for every unit of horizontal distance. The slope is calculated as the ratio of the change in y-coordinates to the change in x-coordinates between two points on the line. It helps us understand the direction and steepness of a line, making it a crucial concept in Coordinate Geometry.