In coordinate geometry, Distance formula is utilized to determine the ratio where a straight line segment is split by a defined point either locally or externally. It’s used to measure the center of mass, center of gravity, centroids and adhoc centers of space rile. A high school student learns different concepts in geometry like transforms, integral geometrical transforms, complex numbers, real numbers, equations and derivatives by learning different formulas. The main problem with this is that students often overlook the real purpose of the formula. Thus, their understanding of the subject suffers.
The main concept of coordinate geometry is that of finding the distance between two points by measuring tangential coordinate planes. To do this, tangent lines are drawn to project the points onto a sphere. The height and horizontal position of the points are then measured along the tangent line. Then these measurements can be transformed into X and Y values and is called the slope intercept form. Here’s an example to explain the concept: Let’s say the central point P is located at (x, y) coordinates.
Let’s try to solve for the values of the tangent lines (P, T). We begin by setting up the tangent lines by drawing them to a section of the sphere so that they lie along the x-axis. We can then use section function and the dot product formulas to define the section of the circle whose radius is (T, x). Using the slopes and intercept functions, we then determine the slope of the tangent on the y-axis and the value of the intercept function is we can use to get the value of the tangent on the x-axis.
The next step is to set up the main coordinate system. This is done by defining two points on the sphere whose distance from one another is zero. These are called the origin of the coordinate system. Now in order to solve for the other two points on the map, we use the distance formula. This works in the same way as the distance formula defined earlier.
The last step in the process of coordinate geometry is to solve for the normal values. The normal values can be found out by dividing the coordinate distance by the normal angle. For instance, if the distance from (x, y) is 10 meters and the normal angle is 40 degrees, then we can find the normal value of the coordinate distance by dividing it by the cosine of the angle. The formula for finding the normal values can be used in conjunction with the section function to get a range of possible normal values.
You can find more details of how to solve for a normal value of a coordinate system in the next lesson. For now, you just have to know that if there are two given points on the coordinate plane then their distance from the center is also given. The distance from (x, y) is the distance from (x+y, y+x). Therefore, the area of the ellipse formed by those two points is also the area of the circle that was inscribed in the x-axis. Finally, if we plug the points (x, y) into the formula for finding the distance, we get the resulting value of the area of the circle.