Coordinate geometry is a topic which combines concepts from algebra, graphs and geometry. Recall how you can describe a line on a graph in terms of y=mx+c ? Coordinate geometry involves describing shapes and their properties in terms of algebraic functions which are plotted onto a graph. In some of our IP Math Tuition classes this week, we are focusing especially on coordinate geometry for an upcoming quiz that our students have!
Core concepts
Equation of a line
As mentioned, any straight line on a graph can be described with the equation y=mx+c. You can find out several things from the equation, including the y-intercept (c) and gradient of the line (m).
A straight line can also be represented in the general form, double-intercept form, and point gradient form. For a refresher on what these are, head on to our earlier article on linear equations and graphs!
Gradient of a line
There are several ways to obtain the gradient of the line. The most common way is to divide the rise (change along y-axis) by the run (change along x-axis). Another method is to use the angle between the line and the positive x-axis to find the gradient, in the formula m=tan(angle).
The gradient of the line can provide information like whether it has a positive slope or negative slope. Perpendicular lines will have gradients that multiply together to give -1. Parallel lines will have the same gradient.
Point on a line
To find the midpoint of a line, you can find the average for each of the x and y values to give the coordinates of the midpoint. Extending this concept, it is also possible to find a point which splits a line in a ratio (e.g. 2 thirds and 1 third).
Area of a triangle/polygon
Considering that a triangle is a polygon with three sides, the formula for area of a triangle is actually just a specific instance of the formula for the area of a polygon. The important point to remember here is that the coordinates should be arranged in the anti-clockwise order.
Sample questions
The ideal way to learn coordinate geometry is to practice with questions. This improves your recall speed for the formulae and also helps you familiarise yourself with various types of questions. Try the questions below to see how you fare!
Conclusion
Coordinate geometry is a very visual topic with quite a few formulae to remember. Besides understanding the concepts and formula, being very careful with calculations is crucial – especially when plugging numbers into the formulae. Quick tip: always check that your answer makes sense! For example, the area of a shape cannot be a negative number – but a gradient CAN be negative!
If math is proving to be a struggle for you, or you simply want to do even better than you already are doing right now, why not consider joining us at Future Academy? We go through topics like this and more in our Secondary Math Tuition classes led by expert math tutors to help students like you feel confident and empowered to excel!