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!
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.