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 (y_{1} – y_{2})/(x_{1} – x_{2})

§ If a line has gradient m and passes through the point (x_{1} ,y_{1}), then the y-intercept of the line is given by c = y_{1} – mx_{1}

§ The mid-point M of the points A(x_{1} ,y_{1}) and B(x_{2} ,y_{2}), has co-ordinates ((x_{1} + x_{2})/2 , (y_{1} + y_{2})/2)

§ The line AB has length AB = √{(x_{2} – x_{1})^{2} + (y_{2} – y_{1})^{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.

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