Math Success Secret: Coordinate Geometry

Monday, June 28

Coordinate Geometry

Coordinate geometry is a branch of geometry. In which two numbers are called coordinates, Coordinate geometry is used to specify the position of a point in a plane and use of algebraic methods in the learning of geometric figures.

The equation of a curve represents the essential property of dissimilar points on the curve, which we locate by means of real numbers. The coordinate geometry is also called as plane Cartesian geometry. Coordinate geometry problems deals with the lines, planes and equations involving in it. These types of problems are easy to solve. Coordinate geometry problems are simple and can be understood easily.

Below are is one example of Coordinate Geometry:

Find the equation of straight line passing through the given points (1, 3) and (3, − 4).

Solution:

We use point slope formula to solve this problem on coordinate geometry

The equation of a straight line is $\displaystyle\frac{{{y}-{y}_{{{1}}}}}{{{y}_{{{1}}}-{y}_{{{2}}}}}$ = $\displaystyle\frac{{{x}-{x}_{{{1}}}}}{{{x}_{{{1}}}-{x}_{{{2}}}}}$
Here (x₁, y₁) = (1, 3) and (x₂, y₂) = (3, − 4).
Substituting the above, the required line is $\displaystyle\frac{{{y}-{3}}}{{{3}+{4}}}$ = $\displaystyle\frac{{{x}-{1}}}{{{1}-{3}}}$
y − 3/7 = x − 1/ (− 2) ⇒ $\displaystyle\frac{{{y}-{3}}}{{{7}}}$ = $\displaystyle\frac{{{x}-{1}}}{{-{2}}}$
⇒ 2(y − 3) = − 7 (x − 1) ⇒ 2y −6 = − 7x + 7
⇒ 7x + 3y = 13.