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Coordinate Geometry Formulas

Coordinate geometry is the study of geometric figures graphed on a coordinate plane. The slope formula can be used to determine whether lines are parallel or perpendicular. The midpoint can be used to determine if segments are bisected and also can be used to find the center of a circle.

When you work in geometry, you sometimes work with graphs, which means you’re working with coordinate geometry. Becoming familiar with the formulas and principles of geometric graphs makes sense, and you can use the following formulas and concepts as you graph: Triangles are at least a third of. Free Geometry worksheets created with Infinite Geometry. Printable in convenient PDF format. Free Geometry Worksheets. Parallel Lines and the Coordinate Plane. Geometry Formula PDF. Memorize the Geometry Formula Sheet with a Free Game. Our online memorization tool, Study Putty, has a game for committing these geometry formulas to memory. You can study coordinate geometry formulas and the formulas for shapes and solids separately or together. We make it easy to do a SAT Math review or some ASVAB study. NCERT Notes For Class 10 Maths Chapter 7: Coordinate Geometry THE CARTESIAN CO-ORDINATE SYSTEM. Let X‘OX and YOY‘ be two perpendicular straight lines meeting at fixed point 0 then X‘OX is called the x—axis and Y‘OY is called the axis of y or y axis. तो आज हम आप लोगो के लिए Mathematics से Related Coordinate Geometry PDF की Notes लेकर आए आए है जो आपके 10+2, और Competition की तैयारी करने के लिए बहुत ही Coordinate Geometry Book PDF Download इस book में आपको SSS Congruence, SAS Congruence, ASA. COORDINATE GEOMETRY IN THREE DIMENSIONS 4.1 Introduction Various geometrical figures in three-dimensional space can be described relative to a set of mutually orthogonal axes O x, Oy, Oz, and a point can be represented by a set of rectangular coordinates (x, y, z).

The following table gives some coordinate geometry formulas. Scroll down the page if you need more explanations about the formulas, how to use the formulas and worksheets to practice.
What is a Coordinate Plane or Cartesian Plane?
The coordinate plane or Cartesian plane is a basic concept for coordinate geometry. It describes a two-dimensional plane in terms of two perpendicular axes: x and y. The x-axis indicates the horizontal direction while the y-axis indicates the vertical direction of the plane. In the coordinate plane, points are indicated by their positions along the x and y-axes.
For example: In the coordinate plane below, point L is represented by the coordinates (–3, 1.5) because it is positioned on –3 along the x-axis and on 1.5 along the y-axis. Similarly, you can figure out the positions for the points M = (2, 1.5) and N = (–2, –3).
How to plot points in the coordinate plane and how to determine the coordinates of points on the coordinate plane?
To graph or plot points, we use two perpendicular lines called axes. The point at which the axes cross is called the origin. Arrows in the axes indicate the positive directions.
Consider the ordered pair (4, 3). The numbers in an ordered pair are called the coordinates. The first coordinate or x-coordinate in this case is 4 and the second coordinate or y-coordinate is 3.
To plot the point (4, 3) we start at the origin, move horizontally to the right 4 units, move up vertically 3 units, and then make a point.
Example:
1. Plot the following points: A(-3,2), B(-1,4), C(-2,-4), D(0,-2), E(3,0)
2. Find the coordinates of the given points

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How to find the slope of a line?
On the coordinate plane, the slant of a line is called the slope. Slope is the ratio of the change in the y-value over the change in the x-value, also called rise over run.

Given any two points on a line, you can calculate the slope of the line by using this formula:

For example: Given two points, P = (0, –1) and Q = (4,1), on the line we can calculate the slope of the line.

What is the Y-intercept?

The y-intercept is where the line intercepts (meets) the y-axis.

For example: In the above diagram, the line intercepts the y-axis at (0,–1). Its y-intercept is equals to –1.

What is the Equation of a Line?
In coordinate geometry, the equation of a line can be written in the form, y = mx + b, where m is the slope and b is the y-intercept. (see a mnemonic for this formula)
For example: The equation of the line in the above diagram is: y = ½ x - 1
How to Find the Slope Given 2 Points?
Example: Find the slope of the two points (-6,3) and (4,-3) How to Write a Slope Intercept Equation for a Line on a Graph?

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What is a Negative Slope?

Let's look at a line that has a negative slope.

For example: Consider the two points, R(0, 2) and S(6, –2) on the line. What would be the slope of the line? What would be the equation of the line?

How to determine the slope of a line given the graph of a line with a negative slope?

How to find the slopes Of Parallel Lines?

In coordinate geometry, two lines are parallel if their slopes (m) are equal.

For example: The line y = ½ x - 1 is parallel to the line y = ½ x + 1 because their slopes are both the same.
How to find the equation of a line parallel to a given line and passing through a given point?
Example: Write the equation of a line that is parallel to the line 2x - 4y = 8 and goes through the point (3, 0). How to find the slopes Of Perpendicular Lines?
In the coordinate plane, two lines are perpendicular if the product of their slopes (m) is –1.
For example: The line y = ½ x - 1 is perpendicular to the line y = –2x – 1. The product of the two slopes is ½ × (-2) = -1.
How to find the slope of a line that is perpendicular to a given line?
Example: Find the slope of the line that is perpendicular to the line 3x + 2y = 6.

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What is the Midpoint Formula?
Some coordinate geometry questions may require you to find the midpoint of line segments in the coordinate plane. To find a point that is halfway between two given points, get the average of the x-values and the average of the y-values.
The midpoint between the two points (x₁,y₁) and (x₂,y₂) is
For example: The midpoint of the points A(1,4) and B(5,6) is
How to derive and use the midpoint formula?
This video gives the formula for finding the midpoint of two points and one example to find the midpoint. What is the Distance Formula

In the coordinate plane, you can use the Pythagorean Theorem to find the distance between any two points.

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The distance between the two points (x₁,y₁) and (x₂,y₂) is

For example: To find the distance between A(1,1) and B(3,4), we form a right angled triangle with A̅B̅ as the hypotenuse. The length of A̅C̅ = 3 – 1 = 2. The length of B̅C̅ = 4 – 1 = 3.
Applying Pythagorean Theorem:

Mathews serial number lookup for guns. I told them I had the receipt and paper work for the purchase of the bow but that didn't matter.

A̅B̅² = 2² + 3²
A̅B̅ = 13
A̅B̅ = √13

How to derive and use the distance formula?
This video shows how the distance formula comes from the Pythagorean Theorem, and one example of finding the distance between two points.

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Coordinate Geometry Notes For Class 10 Chapter 7 Download PDF

NCERT Notes For Class 10 Maths

Chapter 7 : Coordinate Geometry

THE CARTESIAN CO-ORDINATE SYSTEM

Let X‘OX and YOY‘ be two perpendicular straight lines meeting at fixed point 0 then X‘OX is called the x—axis and Y‘OY is called the axis of y or y axis. Point ‗0‘ is called the origin. x axis is known as abscissa and y—axis is known as ordinate.

NOTE : The x- axis and y— axis are mutually perpendicular to each,other that is why, this system of coordinates is also called Rectangular cartesian coordinate system.

QUADRANTS

The coordinate axes X‘OX and Y‘OY devide the plane into four parts, called quadrants, numbered I, II, III and IV anti-clockwise from OX.

NOTE : The coordinates of a point on the x-axis are of the form (x, 0), and of a point on they— axis are of the from (0,y).

DISTANCE FORMULA

The distance between two points whose co—ordinates are P (x₁, y₁) and Q (x₂, y₂) given by the formula √(x₂ — x₁)² + (y₂ — y₁ )²

DISTANCE FROM ORIGIN

√(x — 0)² + (y — 0)² = √x² + y²

NOTE : Since, distance is always non-negative (Positive), we take only the positive square root.

SECTION FORMULA

The coordinates of the point p (x, y) which divides the line segment joining the points A (x₁, y₁) and B (x₂, y₂)

internally in the ratio m₁ : m₂ are x = m₁x₂ +m₂x₁ / m₁ + m₂
and y = m₁y₂ +m₂y₁ / m₁ + m₂
m₁ m₂ / A(x₁. , yx₁) P(x, y) B(x₂, y₂)

NOTE : If the ratio in which P (x, y) divides AB is K : 1, then the coordinates of the point P will be
(kx₂/k + 1 , ky₂ + y₁ / k + 1)

COORDINATES OF MID-POINT

(Special case of section formula)

The mid-point of a line segment divides the line segment in the ratio 1 : 1

* The coordinates of the mid-point P of the join of the points A (x1, y1) and B (x₂, y₂) is

(1.x₁ + 1.x₂ / 1 + 1 , 1.y₁ + 1.y₂ / 1 + 1) =
(x₁ + x₂ / 2 , y₁ + y₂ / 2)

(using section- formula m₁= 1, m₂ = 1)

AREA OF A TRIANGLE

Area of AABC, formed by the points A(x₁ , y₁), B(x₂,y₂), C(x₃, y₃) is given by the numerical value of the expression

1/2 [x₁(y₂ – y₃ + x₂(y₃ – y₁) + x₃(y₁ – y₂)]

NOTE

(1) Area cannot be negative so, we shall ignore negative sign if it occurs in a problem.

(2) To find the area of quadrilateral we shall divide it into two triangles by joining two opposite vertices, find their areas and add them.

(3) If the area of triangle is zero sq. units then the vertices of triangle are collinear.

CENIROID OF A TRIANGLE

The point where the medians of a triangle meet is called the centroid of the triangle. ―If AD is a mediam of the triangle ABC and G is its centroid, then AG/GD = 2/1.‖ The coordinates of the point G are (x₁ + x₂ + x₃ / 3 ,y₁ + y₂ + y₃ / 3)

REMARKS:

(I) Four points will form :
(a) a parallelogram if its opposite sides are equal, but diagonals are unequal.
(b) a rectangle if opposite sides are equal and two diagonals are also equal.
(c) a rhombus if all the four sides are equal, but diagonals unequal,
(d) a square if all sides are equal and diagonals are also equal.

(II) Three points will form:
(a) an equilateral triangle if all the three sides are equal.
(b) an isosceles triangle if any two sides are equal.
(c) a right angled triangle if sum of square of any two sides is equal to square of the third side.
(d) a triangle if sum of any two sides (distances) is greater than the third side (distance).

(III) Three points A, B and C are collinear or lie on a line if one of the following holds
(i) AB + BC — AC
(ii) AC + CB AB
(iii) CA + AB CB.

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Coordinate Geometry Formulas Pdf Free Online

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