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This document contains definitions, facts, formulae and procedures related to coordinate geometry. It includes definitions of x-coordinate and y-coordinate as the distance from the x-axis and y-axis respectively. It provides facts about collinear points and formulas for distance between points, section formula, mid-point formula, and area of a triangle. It outlines procedures for finding the distance between two points using the distance formula and two methods for determining if three points are collinear - checking if the sum of distances between two points equals the third distance, or if the area of the triangle formed is zero.
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- 1. In this document you can review important • Definitions • Facts • Formulae • Procedures Class – X, CBSE MB1007: Coordinate Geometry Learn Math for Free. Visit www.ganitgurooz.com
- 2. What is x-coordinate? Class – X,CBSE MB1007: Coordinate Geometry Important Definitions Topic : x-coordinate Learn Math for Free. Visit www.ganitgurooz.com
- 3. What is x-coordinate? Class – X,CBSE Important Definitions Topic: x-coordinate The distance of a point from the -axis is called its -coordinate, or abscissa. y x Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry
- 4. What is y-coordinate? Class – X,CBSE Important Definitions Topic: y-coordinate Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry
- 5. What is y-coordinate? Class – X,CBSE Important Definitions Topic: y-coordinate The distance of a point from the -axis is called its -coordinate, or ordinate. x y Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry
- 6. Class – X,CBSE Important Facts Topic: Collinear Points Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry Fact # 1 If the area of a triangle formed by joining three points is zero then the points are collinear.
- 7. Class – X,CBSE Important Formulae Topic: Distance Formula 1 1 2 2 2 2 2 1 2 1 The distance between two points , and , is given by the distance formulae . P x y Q x y PQ x x y y Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry
- 8. Class – X,CBSE Important Formulae Topic: Distance Formula 2 2 The distance of a point , from the origin is .P x y x y Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry
- 9. Class – X,CBSE Important Formulae Topic: Section Formula 1 1 2 2 1 2 1 2 2 1 1 2 2 1 1 2 1 2 The coordinates of the point , which divides the line segment joining the points , and , internally in the ratio : are , . P x y A x y B x y m m m x m x m y m y m m m m Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry
- 10. Class – X,CBSE Important Formulae Topic: Section Formula 2 1 2 1 If point P divides AB in the ratio :1, then the coordinates of the point P will be , . 1 1 k kx x ky y k k Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry
- 11. Class – X,CBSE Important Formulae Topic: Section Formula 1 1 2 2 1 2 1 2 The mid-point of the line segment joining the points , and , is given by , . 2 2 P x y Q x y x x y y Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry
- 12. Class – X,CBSE Important Formulae Topic: Area of Triangle 1 1 2 2 3 3 1 2 3 2 3 1 3 1 2 The area of the triangle formed by the points , , , and , is the numerical value of the expression 1 . 2 x y x y x y x y y x y y x y y Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry
- 13. How to find the distance between two points? Class – X,CBSE Important Procedures Topic: Distance Formula Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry
- 14. How to find the distance between two points? Class – X,CBSE Important Procedures Topic: Distance Formula Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry 1 1 2 2 2 2 2 1 2 1 : Identify the formulae for finding the distance between the two points , and , which is given by . x y x y x x y y Step1
- 15. How to find the distance between two points? Class – X,CBSE Important Procedures Topic: Distance Formula Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry 1 1 2 2 2 2 2 1 2 1 : Identify the formulae for finding the distance between the two points , and , which is given by . x y x y x x y y Step1 1 2 1 2: Note down the given coordinates of each point i.e. , , , .x x y yStep 2
- 16. How to find the distance between two points? Class – X,CBSE Important Procedures Topic: Distance Formula Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry 1 1 2 2 2 2 2 1 2 1 : Identify the formulae for finding the distance between the two points , and , which is given by . x y x y x x y y Step1 1 2 1 2: Note down the given coordinates of each point i.e. , , , .x x y yStep 2 : Substitute these values in the distance formulae.Step 3
- 17. How to find the distance between two points? Class – X,CBSE Important Procedures Topic: Distance Formula Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry 1 1 2 2 2 2 2 1 2 1 : Identify the formulae for finding the distance between the two points , and , which is given by . x y x y x x y y Step1 1 2 1 2: Note down the given coordinates of each point i.e. , , , .x x y yStep 2 : Substitute these values in the distance formulae.Step 3 : Solve and find the distance between the two points.Step 4
- 18. How to check if given three points are collinear or not (Method 1)? Class – X,CBSE Important Procedures Topic: Collinearity of Three Points Learn Math for Free. Visit www.ganitgurooz.com MB1007: Coordinate Geometry
- 19. How to check if given three points are collinear or not (Method 1)? Class – X,CBSE Important Procedures Topic: Collinearity of Three Points Learn Math for Free. Visit www.ganitgurooz.com : The question identify the given three points A, B and C.Step 1 MB1007: Coordinate Geometry
- 20. How to check if given three points are collinear or not (Method 1)? Class – X,CBSE Important Procedures Topic: Collinearity of Three Points Learn Math for Free. Visit www.ganitgurooz.com :The question identify the given three points A, B and C.Step 1 MB1007: Coordinate Geometry 2 2 2 1 2 1: Use the distance formulae for finding the distance between the three points that is to find the length AB, BC and AC. x x y yStep 2
- 21. How to check if given three points are collinear or not (Method 1)? Class – X,CBSE Important Procedures Topic: Collinearity of Three Points Learn Math for Free. Visit www.ganitgurooz.com : The question identify the given three points A, B and C.Step 1 MB1007: Coordinate Geometry 2 2 2 1 2 1: Use the distance formulae for finding the distance between the three points that is to find the length AB, BC and AC. x x y yStep 2 3: Check if the sum of lengths of any two line segments is equal to the length of the third line segment.Step
- 22. How to check if given three points are collinear or not (Method 1)? Class – X,CBSE Important Procedures Topic: Collinearity of Three Points Learn Math for Free. Visit www.ganitgurooz.com : The question identify the given three points A, B and C.Step 1 MB1007: Coordinate Geometry 2 2 2 1 2 1: Use the distance formulae for finding the distance between the three points that is to find the length AB, BC and AC. x x y yStep 2 : Check if the sum of lengths of any two line segments is equal to the length of the third line segment.Step 3 : If this is true then the given points are collinear or else they are not collinear.Step 4
- 23. How to check if given three points are collinear or not (Method 2)? Class – X,CBSE Important Procedures Topic: Collinearity of Three Points Learn Math for Free. Visit www.ganitgurooz.com : From the question identify the given three points A, B and C.Step 1 MB1007: Coordinate Geometry
- 24. How to check if given three points are collinear or not (Method 2)? Class – X,CBSE Important Procedures Topic: Collinearity of Three Points Learn Math for Free. Visit www.ganitgurooz.com : From the question identify the given three points A, B and C.Step 1 MB1007: Coordinate Geometry 1 2 3 2 3 1 3 1 2 : Find the area of the triangle formed by these three points using the area formulae 1 . 2 x y y x y y x y y Step 2
- 25. How to check if given three points are collinear or not (Method 2)? Class – X,CBSE Important Procedures Topic: Collinearity of Three Points Learn Math for Free. Visit www.ganitgurooz.com : From the question identify the given three points A, B and C.Step 1 MB1007: Coordinate Geometry 1 2 3 2 3 1 3 1 2 : Find the area of the triangle formed by these three points using the area formulae 1 . 2 x y y x y y x y y Step 2 : If the area of the triangle is equal to zero then the given points are collinear otherwise they are not collinear. Step 3