OCR Advanced FSMQ - Additional Maths

6.10 Condition for two straight lines to be perpendicular to each other When two lines are perpendicular to each other (i.e. they make an angle of 90°), the product of their gradients is −1. If one line has a gradient m 1 and the other a gradient of m 2 then m 1 m 2 = −1 if the lines are perpendicular to each other. For example, if a straight line has gradient −  1 3 then the gradient of the line perpendicular to this is given by ( −  1 3 ) m 2 = −1, hence gradient m 2 = 3 6.11 Determining the equation of a line that is parallel to another line Parallel lines have the same gradient and you are often asked to find the equation of a line that is parallel to another line. Here you simply take the gradient of the parallel line and use it with a point on the other line to find the equation of the other line. Examples 9 Find the equation of line L 1 which passes through the point (1, 2) and is parallel to the line L 2 which has equation 2 x − y + 1 = 0. Answer 9 First find the equation of the line L 2 in the form y = mx + c 2 x − y + 1 = 0 So y = 2 x + 1 Hence the gradient of L 2 = 2. Since lines L 1 and L 2 are parallel, they both have the same gradient of 2. Comparing this equation with y = mx + c gives the gradient, m = 2. 6 Coordinate geometry of straight lines 131