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The study of geometry using a coordinate system to examine the features and relationships of geometric forms is called coordinate geometry, at times referred to as analytical geometry. Because it enables students to carefully explore forms, lines, and curves using coordinates on the Cartesian plane, it is a crucial topic in mathematics for Class 10.
The fundamental idea is to use algebraic equations to depict geometric figures and their relationships. Students in class 10 need to concentrate on understanding lines, points, and the separation between two points. This serves as the foundation for advanced studies in mathematics. With key ideas, formulas, and examples, the piece offers an extensive understanding of Class 10 Coordinate Geometry Notes.
Class 10 coordinate geometry chapter 7 notes cover all the main concepts like the distance formula, Collinearity Condition, section formula, and many others. The downloadable notes PDFs for Coordinate Geometry are provided below in detailed and easy-to-understand language.
Students can attempt a chapter 7 class 10 maths coordinate geometry worksheet to prepare themselves as per the exam pattern. Below we have provided the links to downloadable PDFs of DoE Worksheets for class 10 Mathematics to practice more questions.
Below we have provided the links to a downloadable PDF of Experiential Learning Activity for class 10 maths coordinate geometry to help students implement their acquired knowledge in the real world.
Below we have provided the links for Mathematics coordinate geometry class 10 formulas to help students solve complex questions and understand the concepts easily.
Below we have provided the links to downloadable PDFs of Mind maps for coordinate geometry class 10 Mathematics to help students implement their acquired knowledge in the real world.
Below we have provided Class 10 Mathematics Important Questions that cover questions from the NCERT textbook.
Below we have provided Class 10 Mathematics Question Banks that cover every typology question with detailed explanations from various resources in one place.
Below we have provided Class 10 Mathematics Support Material that covers Case Study-based questions from the various concepts explained in Mathematics NCERT chapters.
The coordinate geometry depends upon the Cartesian plane that uses the ordered pairs as (x, y) in representing points. The coordinates indicate where the point lies on the Cartesian plane. Two perpendicular axes form the plane.
The point of intersection between the X-axis and the Y-axis is called the origin (0, 0). The horizontal axis represents the value of the x-coordinate and the vertical axis represents the value of the y-coordinate.
The distance between two points is one of the fundamental concepts in coordinate geometry. The distance formula is used to find the straight-line distance between two points P(x1, y1) and Q(x2, y2) on the Cartesian plane.
Formula:
The distance d between the points (x1, y1) and (x2, y2) is given by:
d=√((x2 – x1)² + (y2 – y1)²)
This distance formula is based on the Pythagorean Theorem, where the horizontal and vertical differences are the two perpendicular sides of a right triangle, and the distance is the hypotenuse.
Example:
Find the distance between the points A(1, 2)and B(4, 6).
Solution:
d = √((4– 1)² + (6 – 2)²)
= √(3)² + (4)²
= √(9 + 16)
= √(25)
= 5
So, the distance between points A and B is 5 units.
The section formula is used to find the coordinates of a point that divides a line segment in a certain ratio. It has many applications in many geometric problems, such as finding the midpoints or how to divide a line segment according to a given ratio.
Formula:
The coordinates P(x, y) of a point which divides the line segment joining A(x1, y1) and B(x2, y2) in the ratio m:n are given by,
x = (n x1 + m x2) / (m + n),
y = (n y1 + m y2) / (m + n)
In the above equations, m and n are the ratios in which the point is dividing the segment.
Example:
Find the coordinates of the point that divides the segment joining A(1, 2) and B(4, 6) in the ratio 2:3.
Using the section formula:
Solution:
x = 3(1) + 2(4) / 2 + 3
= 3 + 8 / 5
= 11 / 5
y = 3(2) + 2(6) / 2 + 3
= 6 + 12 / 5
= 18 / 5
Thus, the coordinates of the point dividing the segment in the ratio 2:3 are (11/5, 18/5).
The midpoint formula is a special type of section formula, where the line segment is divided into two equal parts, that is, a 1:1 ratio. Midpoint of a segment is a point that divides the segment exactly in the middle between the two endpoints.
Formula:
The coordinates of a midpoint M(x, y) from a given line segment connecting A(x1, y1) and B(x2, y2) are given by the relation:
x = (x1 + x2) / 2, y = (y1 + y2) / 2
Example:
Find the midpoint of the segment joining A(1, 2) and B(4, 6).
Solution:
x = (1 + 4) / 2
= 5 / 2, y
= (2 + 6) / 2
= 8 / 2
= 4
Thus, the midpoint of the segment is (5/2, 4).
The slope of a line measures the steepness of the line. It is obtained by calculating the difference along the vertical axis divided by the difference along the horizontal axis. The concept of slope is necessary to understand the equation of a straight line.
Formula:
The slope m of a line passing through two points A(x1, y1) and B(x2, y2) can be written as follows:
m = (y2 - y1) / (x2 - x1)
Example:
Find the slope of the line passing through A(1, 2) and B(4, 6).
Solution:
m = (6 - 2) / (4 - 1)
= 4 / 3
So, the slope of the line is 4/3.
There are various forms of equations for a line, depending on the information given. The most commonly used forms in Class 10 are:
The equation of a line with slope m and y-intercept c is given by:
y = mx + c
This form is useful when you know the slope and the y-intercept of the line.
If the slope of the line is m and it passes through the point (x1, y1), the equation can be written as:
(y - y1) = m(x - x1)
When there are two given points on the line (x1, y1) and (x2, y2), then the equation can be written in the following form:
(y - y1) / (y2 - y1) = (x - x1) / (x2 - x1)
Example:
Find the equation of the line passing through the points A(1, 2) and B(4, 6).
Solution:
First, calculate the slope:
m = 6 - 2 / 4 - 1 = 4 / 3
Now, using the point-slope form with point A(1, 2):
y - 2 = 4/3 (x - 1)
Thus, the equation of the line is:
y - 2 = 4/3 (x - 1)
Expanding:
y - 2 = 4/3x - 4/3
y = 4/3x - 4/3 + 2
y = 4/3x + 2/3
Thus, the equation of the line is y = 4/3x + ⅔.
Coordinate geometry is more than just distance, midpoint, or line equations; it has many applications. Some of the main applications are as follows:
Calculating the area of a triangle
Use the coordinates of the three vertices to determine the area with the formula:
Area = ½ | x1 (y2 - y3) + x2 (y3 - y1) + x3 (y1 - y2) |
Geometric properties of shapes
Coordinate geometry can be used to show properties such as the collinearity of points and the concurrency of lines.
Practical application in real life
This branch of mathematics is used in various domains, including physics (for motion analysis), engineering, architecture, and computer graphics.
Coordinate geometry is an area of mathematics, which helps students understand geometric concepts through algebraic methods. Using the distance formula, midpoint formula, section formula, and equation of a line, students can solve a variety of problems. The subject not only improves mathematical ability but also provides the basis for complex topics in mathematics and science. With regular practice and problem-solving, students can develop a strong understanding of coordinate geometry to help them be successful in Class 10 and further studies.
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