Analytic Geometry

Analytic Geometry is a branch of algebra, a great invention of Descartes and Fermat, which deals with the modelling of some geometrical objects, such as lines, points, curves, and so on. It is a mathematical subject that uses algebraic symbolism and methods to solve the problems. It establishes the correspondence between the algebraic equations and the geometric curves. The alternate term which is used to represent the analytic geometry is “coordinate Geometry”.

It covers some important topics such as midpoints and distance, parallel and perpendicular lines on the coordinate plane, dividing line segments, distance between the line and a point, and so on. The study of analytic geometry is important as it gives the knowledge for the next level of mathematics. It is the traditional way of learning the logical thinking and the problem solving skills. In this article, let us discuss the terms used in the analytic geometry, formulas, Cartesian plane, analytic geometry in three dimensions, its applications, and some solved problems.

What is the point of intersection of the axis (X-axis and Y-axis) called?

Solution:

The point of intersection of the axis (X-axis and Y-axis) called Origin and X and the Y-axis is 0 at this point.

Example 2:

Find the distance between two points A and B such that the coordinates of A and B are (5, -3) and (2, 1).

Solution:

Given that, the coordinates are:

A = (5, -3)  = (x1, y1)

B = (2, 1) = (x2, y2)

The formula to find the distance between two points is given as:

Distance, d = √[(x2– x1)2 + (y2– y1)2]

d = √[(2 – 5)2 + (1- (-3))2]

d = √[(-3)2 + (4)2]

d = √[9 + 16]

d = √(25)

d = 5

Thus, the distance between two points A and B is 5 units.

Example 3:

Determine the slope of the line, that passes through the point A(5, -3), and it meets y-axis at 7.

Solution:

Given that, the point is A = (5, -3)

We know that, if the line intercepts at y-axis, then x2 = 0

Thus, (x2, y2) = (0, 7)

The formula to find the slope of a line is:

m = (y2 –y1)/ (x2 -x1)

Now, substitute the values

m = (7- (-3))/(0 – 5)

m = 10/-5

m = -2

Therefore, the slope of the line is -2.

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