Coordinate geometry formulas

Coordinate geometry, often known as analytic geometry, is a branch of mathematics that illustrates the relationship between geometry and algebra using graphs and the use of curves and lines. It gives geometrical aspects in Algebra, allowing difficult geometrical problems to be solved. It’s a type of geometry in which the coordinates of points on a plane are represented by an ordered pair of numbers.

The study of geometry using coordinate points is known as coordinate geometry or Cartesian geometry. Various computations in geometry can be done quickly and conveniently with the help of coordinate geometry.

Here are a few suggestions:

• Calculating the distance between two spots
• Dividing the line in the given m:n ratio
• Finding the line’s midpoint.
• Calculating a triangle’s area in a Cartesian plane, and so on.

Coordinates of a Point

A point’s coordinates are a pair of numbers that specify its precise location on a two-dimensional plane. Remember that the coordinate plane has two axIs, the x and y axis, that are at right angles to each other. The coordinates of a point indicate how far along each axis it is situated.

Formulas of coordinate geometry

Coordinate geometry formulas make it easier to prove the many qualities of lines and figures represented by coordinates. The distance formula, slope formula, midpoint formula, section formula, and line equation are all coordinate geometry formulas

Distance Formula:  Two points are A and B, with coordinates (x,y), and (x,y) equals the square root of the sum of the squares of the difference of x and y coordinates.

Slope Formula: The angle of a surface or a line is known as a slope. For slope calculation, the angle formed by the lines with the positive axis must be known, or any two locations on the line can be used as a reference. 

Assume that a slope is inclined at an angle wih the positive x-axis, such that

Slope (m) =Tanθ

Alternatively, if (x₁ ,y₁ )and (x₂ ,y₂ )are the two points on the line,

Slope (m) =(y₂–y₁) / (x₂–x₁)

Midpoint Formula: The midpoint is located exactly in the middle of the two points. Take two points A and B with coordinates (x,y) to calculate the midpoint of a line joining them (x,y). also, consider M(x,y) to be the line’s midpoint. For the given points A and B, the midpoint formula will be,

Area of triangle formula: When all three vertices of a triangle are known in coordinate geometry, the area of the triangle can be calculated. The three vertices of a triangle are (x, y), & (x, y). The area of the object can then be calculated using the formula,

Centroid of a Triangle formula

The point of intersection of a triangle’s medians is the triangle’s centroid. The vertices of a triangle are found at the triangle’s centroid. A(x₁,y₁), B(x₂,y₂), C(x₃,y₃), is calculated using the formula below.

Coordinate geometry line formula 

The following is a list of line equations:

Standard form:                   Ax+By=c

The real numbers are A,B,& C, and neither A nor B are equal to zero.

Point slope form:      y-y₁=m(x-x₁)  

A point on the line is (x₁ , y₁), and the slope of the line is m.

Slope intercept form: y=mx+b

The slope of the line is m, and the y-interceptt value is b.

Coordinate geometry formulas Examples 

Example 2: Determine the equation of a line with a slope of -1 that passes through (-2,3).

Solution: (x₁,y₁)=(-2,3) is the point of line and slope is m=-1

We can write the equation of the line in coordinate geometry point and slope form as follows:

(y-y₁) = m(x-x₁)

(y-3) =(-1)(x-(-2))

y-3 = -(x+2)

y-3 = -x-2

x+y = 3-2

x+y = 1

As a result, x + y = 1 is the equation of the line.

How to remember coordinate geometry formulas

Some tips on how to learn or remember coordinate geometry formulas are given below.

• Problems involving coordinate geometry should not be practised without the use of figures.
• The formulas should be written in a separate notebook. Keep a running list of all essential formulas you encounter while learning.
• Make a list of all the formulas you can remember.
• To know what the question is asking for, a careful reading of the question is required, which will save time.
• It’s best to avoid referring to multiple books for the same idea to avoid confusion. One standard book and one reference book should be enough.

Conclusion

We learn about coordinate geometry formulas, coordinate geometry line formulas, and suggestions for remembering formulas in this article. Coordinate geometry is required to provide a link between algebra and geometry by the use of line and curve graphs. It is an important part of mathematics that helps us locate points on a plane. It also has various uses in trigonometry, calculus, dimensional geometry, and other sciences. And coordinate geometry formulas  are used to determine the midpoint of a line, determine the distance between two points, and split lines in the m:n ratio.