Coordinate geometry: Distance and section formula

Coordinate Geometry: Distance and Section Formula Coordinate geometry is a branch of geometry concerned with the relationship between coordinates of points...

Coordinate Geometry: Distance and Section Formula

Coordinate geometry is a branch of geometry concerned with the relationship between coordinates of points in a plane. This branch allows us to measure distances between points, determine the lengths of lines and curves, and identify the areas of geometric figures.

Distance Formula:

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Section Formula:

The area of a geometric figure is given by the formula:

$A = \frac{1}{2} \text{base} \times \text{height}$

where the base and height are the lengths of the base and the height of the figure, respectively.

Examples:

If two points are located at $(3, 4)$ and $(7, 10)$ , then the distance between them is 7 units.
The area of a triangle with a base of 5 cm and a height of 3 cm is 7.5 cm².
The circumference of a circle with a radius of 3 cm is 18 cm