Maths Lore by Miss Rafa

Coordinate Geometry is Unit 3 from IGCSE 0580 Syllabus for the examination period of 2025 to 2027. Aspects that will be explored: 3.1 Coordinates  3.2 Drawing Linear Graph   3.3  Equation &  Gradient of Linear Graph 3.4 Length & Midpoint  3.5 Parallel Lines & Perpendicular Lines  Shall we explore the lore behind Coordinate Geometry? It all begins with an ill French Man that was bedridden. Let's watch the video before diving into the topic.

 Parallel Lines  In a graph, the properties of parallel lines share the same gradient. As the slope doesn't change m remains the same for both line equations. Perpendicular Line A perpendicular line is a line that bisects another line, going through the midpoint creating a right angle at the point of intersection  The formula to calculate the gradient for perpendicular line  As we have reached the end of the unit 3  Past Year Paper Questions 

 Calculating the Length of the Line To find the length of the starting coordinate and the ending coordinate of the line. Similar to gradient we will need two coordinates to figure out the length. The length formula is derived from the Pythogoras theorem formula. The diagram below demonstrates it.   As from the diagram above,  it creates a right-angle triangle. Hence, using a modified variation of the Pythogares theorem.  Calculating the Midpoint of the Line Similar to length a starting coordinate and ending coordinate of the line is required. The midpoint formula is in the coordinate format. 

 Equation of Linear Graph  y and x are the variables while m is the gradient Gradient dictates how steep or flat the line is. While y-intersect is the point where the line crosses the y-axis.  Calculating Gradient  Gradient defines how steep or flat the line will be. In the line equation, the gradient is represented with m.  The gradient is also referred to as the slope.  To find the gradient (m) we need 2 coordinates.  If a diagram is given, asking you to calculate you can simply count the vertical distance between 2 coordinates count the horizontal distance, and calculate as shown below. An alternative way to solve without using the formula or calculator is by taking 2 exact coordinates when a diagram is given. creating a right-angle triangle, counting from the point horizontally and then vertically. Horizontally if going right it is positive if left negative. similarly vertically going up is positive and going down is negative. As explained by th...

  What is a Linear Graph? Linear the word itself means straight . This is a line drawn in a graph that has no curves. To draw the linear graph we have to plot coordinates.  Usually, an equation is given in the line equation format: The equation will always have 2 variables x and y. The linear equation will always have a positive x or a negative x.  When y=x ( positive)   When y=-x (negative) Some Special Cases  When:   y= 4 (Blue Line)    y= 1 (Green Line)    y= -2 ( Red Line)  When:   x= 4 (Blue Line)    x= 1 (Green Line)    x= -2 ( Red Line)    How to Draw a Linear Graph? The question would have an equation with 2 unknown variables x and y. Examples:  a) 2x-y=4 b) y-x=9 c) x= 3y-6 d) y= -7x-3 Step 1 : Check if the question gives a range such as  -4 ≤ x ≤ 4. This indicates x-axis should be from -4 to 4. Draw the x-axis and y-axis on graph paper accordingly. Step 2: Draw a table of value...

Coordinates are always written in (x, y) format in cartesian plane. Coordinates are also refereed to as an ordered pair. This gif below shows how to determine coordinates.  Step 1: Identify the point on the x-axis for the x coordinate.  Step 2: Identify  the point on y-axis of the y-coordinate. Step 3 : ( x-coordinate, y-coordinate)  Try the Kahoot Quiz  to check your knowledge.  If you'd like a little extra help attempt the  Practice Worksheet