In part 3 of this series, I have listed what you need to know well about co-ordinate geometry and straight lines  in order to get your A Level studies off to a good start.

Co-ordinate Geometry

Straight lines

§        The equation of a straight line is of the form y = mx + c where m is the gradient of the line and c is the y-intercept (where the line crosses the y-axis)

§        Given the co-ordinates of two points on a line, you can find the gradient, m, of the line using the formula (difference in y values)/(difference in x-values) or (y1 – y2)/(x1 – x2)

§        If a line has gradient m and passes through the point (x1 ,y1), then the y-intercept of the line is given by c = y1 – mx1

§        The mid-point M of the points A(x1 ,y1) and B(x2 ,y2), has co-ordinates ((x1 + x2)/2 , (y1 + y2)/2)

§        The line AB has length AB = √{(x2 – x1)2 + (y2 – y1)2}

§        Two straight lines are parallel if they have equal gradients

§        Two straight lines are perpendicular if they are at right angles to each other

§        If a line L has gradient m, then the gradient of any line perpendicular to L is –1/m provided that m≠0


Knowing and being able to use and apply all of the above will be essential in your A Level studies. If you are unsure about any of these basics involving straight lines, make sure you look at the topic again before September.