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BEAUTY HOLIDAY UK 3) CORDINATE GEOMETRY Points: There are two axes in coordinate geometry: Horizontal axis called X – axis Vertical axis called Y – axis First you read X value and then Y value For example the point A(20, 15) means X = 20, Y = 15 Example: Coordinate axis divided into four quadrants (sections) The distance between two points: The distance between two points A(x1,y1) and B(x2,y2) can be obtained as: Horizontal distance = x2 – x1 Vertical distance = y2 – y1 Example: Find the area of the following right angled triangle: The area of right angled triangle is given by: Area = ½ x b x h = ½ x (x2 – x1) x (y2 – y1) Example: Find the distance between the following two points Distance = x2 – x1 = 5 – 2 = 3 units Example: Find the area and perimeter of the following rectangle. They both have slope = 3 The larger the slope, the steeper is the line. The straight line will either intersect the x – axis, the y – axis or both Points of intersections: The point of intersection is x = 3, y = 1 From the figure below, what are the points of intersection between the line and the graph? The points of intersection are: x = 2, y = -1 and x = -3, y = 4 Example: What are the points of intersection of the line y = 2x – 4 and the graph y = 4 – x2? (use the diagram below): The points of intersection are: (2,0) and (-4, -12) Graph interpretations: Consider the graph x = constant, say x = -5. This means that: x does not change y can take any number Consider the graph y = x The values of x and y are always the same anywhere along the line.