## How do you do proofs in coordinate geometry?

When developing a coordinate geometry proof:

- Plot the points, draw the figure and label.
- State the formulas you will be using.
- Show ALL work.
- Have a concluding sentence stating what you have proven and why it is true. Usually a theorem or a definition is needed here.

**How useful is coordinate geometry in real life?**

Air traffic is managed and regulated by using coordinate geometry. Coordinates of the flight are used to describe its current location of the aircraft. Even if an aircraft moves a small distance (up, down, forward or backward), the coordinates of flight are updated in the system for every slight change in its position.

### How do we verify the properties of geometric figures using coordinate geometry?

When you draw a geometric figure on a coordinate grid, you can verify many of its properties using the properties of lines and line segments. You can use the midpoint formula to determine whether a point bisects a line segment.

**What is the first step in a coordinate geometry proof?**

Coordinate geometry can also be used to prove conjectures. A coordinate proof is a style of proof that uses coordinate geometry and algebra. The first step of a coordinate proof is to position the given figure in the plane. You can use any position, but some strategies can make the steps of the proof simpler.

#### How can coordinate proof be used to prove two lines are parallel?

Note they are parallel when the slopes are the same. When two straight lines are plotted on the coordinate plane, we can tell if they are parallel from the slope, of each line. If the slopes are the same then the lines are parallel.

**Who is the father of coordinate geometry?**

RenĂ© Descartes

The invention of Cartesian coordinates in the 17th century by RenĂ© Descartes (Latinized name: Cartesius) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra.

## What are the applications of coordinate geometry?

Applications of coordinate geometry

- It is used to find the distance between two points.
- It is used to find the ratio of dividing lines in the m:n ratio.
- It is used to find the mid-point of a line.
- It is used to calculate the area of a triangle in the Cartesian plane.

**What is the significance of coordinate proof in proving geometric properties?**

The coordinate proof is a proof of a geometric theorem which uses “generalized” points on the Cartesian Plane to make an argument. The method usually involves assigning variables to the coordinates of one or more points, and then using these variables in the midpoint or distance formulas .