Page 1 (Coordinate geometry is used to locate the position of a point on a plane with the help of a pair of coordinate axes) 1. Coordinate Axes: Let and be two perpendicular lines intersecting at O. The point O is called the origin and (x-axis) and (y-axis) are called coordinate axes. 2. The distance of a point from the x-axis is called its y-coordinate, or ordinate. 3. The distance of a point from the y-axis is called its x-coordinate, or abscissa. 4. Distance formula: a. Distance between two points [suppose, A( ) and B( )] on a plane Page 2 (Coordinate geometry is used to locate the position of a point on a plane with the help of a pair of coordinate axes) 1. Coordinate Axes: Let and be two perpendicular lines intersecting at O. The point O is called the origin and (x-axis) and (y-axis) are called coordinate axes. 2. The distance of a point from the x-axis is called its y-coordinate, or ordinate. 3. The distance of a point from the y-axis is called its x-coordinate, or abscissa. 4. Distance formula: a. Distance between two points [suppose, A( ) and B( )] on a plane ( ) ( ) v( ) ( ) Note: Since distance is always non-negative, we take only the positive value of the square root. b. Distance of a point A( ) from the origin O( ) on a plane. v Page 3 (Coordinate geometry is used to locate the position of a point on a plane with the help of a pair of coordinate axes) 1. Coordinate Axes: Let and be two perpendicular lines intersecting at O. The point O is called the origin and (x-axis) and (y-axis) are called coordinate axes. 2. The distance of a point from the x-axis is called its y-coordinate, or ordinate. 3. The distance of a point from the y-axis is called its x-coordinate, or abscissa. 4. Distance formula: a. Distance between two points [suppose, A( ) and B( )] on a plane ( ) ( ) v( ) ( ) Note: Since distance is always non-negative, we take only the positive value of the square root. b. Distance of a point A( ) from the origin O( ) on a plane. v 5. Section formula: a. The coordinates of the point A( ) which divides the line segment PQ [where, P( ) and Q( )], internally, in the ratio are ( ) Note: The coordinates of the point A( ) can also be derived by drawing perpendiculars from P, A and Q on the y-axis and proceeding as above. b. If the ratio in which A( ) divides PQ is k : 1, then the coordinates of the point A will be Page 4 (Coordinate geometry is used to locate the position of a point on a plane with the help of a pair of coordinate axes) 1. Coordinate Axes: Let and be two perpendicular lines intersecting at O. The point O is called the origin and (x-axis) and (y-axis) are called coordinate axes. 2. The distance of a point from the x-axis is called its y-coordinate, or ordinate. 3. The distance of a point from the y-axis is called its x-coordinate, or abscissa. 4. Distance formula: a. Distance between two points [suppose, A( ) and B( )] on a plane ( ) ( ) v( ) ( ) Note: Since distance is always non-negative, we take only the positive value of the square root. b. Distance of a point A( ) from the origin O( ) on a plane. v 5. Section formula: a. The coordinates of the point A( ) which divides the line segment PQ [where, P( ) and Q( )], internally, in the ratio are ( ) Note: The coordinates of the point A( ) can also be derived by drawing perpendiculars from P, A and Q on the y-axis and proceeding as above. b. If the ratio in which A( ) divides PQ is k : 1, then the coordinates of the point A will be ( ) c. If the ratio in which A( ) divides PQ is 1 : 1, then the coordinates of the mid- point A will be (Also known as the Mid-point formula) ( ) ( ) Page 5 (Coordinate geometry is used to locate the position of a point on a plane with the help of a pair of coordinate axes) 1. Coordinate Axes: Let and be two perpendicular lines intersecting at O. The point O is called the origin and (x-axis) and (y-axis) are called coordinate axes. 2. The distance of a point from the x-axis is called its y-coordinate, or ordinate. 3. The distance of a point from the y-axis is called its x-coordinate, or abscissa. 4. Distance formula: a. Distance between two points [suppose, A( ) and B( )] on a plane ( ) ( ) v( ) ( ) Note: Since distance is always non-negative, we take only the positive value of the square root. b. Distance of a point A( ) from the origin O( ) on a plane. v 5. Section formula: a. The coordinates of the point A( ) which divides the line segment PQ [where, P( ) and Q( )], internally, in the ratio are ( ) Note: The coordinates of the point A( ) can also be derived by drawing perpendiculars from P, A and Q on the y-axis and proceeding as above. b. If the ratio in which A( ) divides PQ is k : 1, then the coordinates of the point A will be ( ) c. If the ratio in which A( ) divides PQ is 1 : 1, then the coordinates of the mid- point A will be (Also known as the Mid-point formula) ( ) ( ) 6. Area of a triangle: a. The area of a triangle formed by the points P( ), Q( ) and R( ) is the numerical value of the expression [ ( ) ( ) ( )]Read More

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