text: • # Revision:Coordinate Geometry
  
  TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Coordinate Geometry
  
  ## The distance between two points
  
  The length of the line joining the points and is:
  
  ### Example
  
  Find the distance between the points (5, 3) and (1, 4).
  
  Distance =
  
  If you think about this, it's just Pythagoras and what we are finding is the hypotenuse or distance in this case.
  
  ## The midpoint of a line joining two points
  
  The midpoint of the line joining the points and is
  
  ### Example
  
  Find the coordinates of the midpoint of the line joining (1, 2) and (3, 1).
  
  Midpoint =
  
  ## The gradient of a line joining two points
  
  The gradient m of the line joining the points and is:
  
  ### Example
  
  Find the gradient of the line joining the points (5, 3) and (1, 4).
  
  ## The equation of a line using one point and the gradient
  
  The equation of a line which has gradient m and which passes through the point is:
  
  ### Example
  
  Find the equation of the line with gradient 2 passing through (1, 4).
  
  Since the equation of a line passing through and can be written:
  
  ## Perpendicular Lines
  
  We can work out the equation of a perpendicular line by using the relationship:
  
  This means to find the gradient of a perpendicular line we take the reciprocal of the original line with it's sign changed.
  
  ### Example
  
  Find the equation of the line perpendicular to the line, which passes through the points (1, 3) and (4,9), and goes through the origin.
  First, find the equation of the original line:
  
  To find the perpendicular line, we use , giving a gradient of -1/2. We then use the straight line formula to find the equation.
  
  Try Learn together, TSR's study area
  
  32,949
  revision notes
  
  35,728
  mindmaps
  
  34,716
  crosswords
  
  14,332
  quizzes
  
  create
  a study planner
  
  thousands
  of discussions
  
  Today on TSR
explanation: The provided text is a set of revision notes on coordinate geometry. It covers topics such as the distance between two points, the midpoint of a line joining two points, the gradient of a line joining two points, the equation of a line using one point and the gradient, and perpendicular lines. Each topic includes a formula and an example.
  
  The text contains multiple questions and their corresponding answers.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: • # Revision:Coordinate Geometry
  
  TSR Wiki > Study Help > Subjects and Revision > Revision Notes > Mathematics > Coordinate Geometry
  
  ## The distance between two points
  
  The length of the line joining the points and is:
  
  ### Example
  
  Find the distance between the points (5, 3) and (1, 4).
  
  Distance =
  
  If you think about this, it's just Pythagoras and what we are finding is the hypotenuse or distance in this case.
  
  ## The midpoint of a line joining two points
  
  The midpoint of the line joining the points and is
  
  ### Example
  
  Find the coordinates of the midpoint of the line joining (1, 2) and (3, 1).
  
  Midpoint =
  
  ## The gradient of a line joining two points
  
  The gradient m of the line joining the points and is:
  
  ### Example
  
  Find the gradient of the line joining the points (5, 3) and (1, 4).
  
  ## The equation of a line using one point and the gradient
  
  The equation of a line which has gradient m and which passes through the point is:
  
  ### Example
  
  Find the equation of the line with gradient 2 passing through (1, 4).
  
  Since the equation of a line passing through and can be written:
  
  ## Perpendicular Lines
  
  We can work out the equation of a perpendicular line by using the relationship:
  
  This means to find the gradient of a perpendicular line we take the reciprocal of the original line with it's sign changed.
  
  ### Example
  
  Find the equation of the line perpendicular to the line, which passes through the points (1, 3) and (4,9), and goes through the origin.
  First, find the equation of the original line:
  
  To find the perpendicular line, we use , giving a gradient of -1/2. We then use the straight line formula to find the equation.
  
  Try Learn together, TSR's study area
  
  32,949
  revision notes
  
  35,728
  mindmaps
  
  34,716
  crosswords
  
  14,332
  quizzes
  
  create
  a study planner
  
  thousands
  of discussions
  
  Today on TSR
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The provided text is a set of revision notes on coordinate geometry. It covers topics such as the distance between two points, the midpoint of a line joining two points, the gradient of a line joining two points, the equation of a line using one point and the gradient, and perpendicular lines. Each topic includes a formula and an example.
  
  The text contains multiple questions and their corresponding answers.
  
  Label: multiple-question-and-answer