OCR Advanced FSMQ - Additional Maths

Exam practice 1 A line passes through the points A (1, −1) and B (3, 4). (a) Find the gradient of line AB . (b) Find the coordinates of C , the mid-point of AB . (c) The line L is perpendicular to line AB and passes through the point C . Find the equation of line L . Answer 1 (a) Gradient = y 2 − y 1 x 2 − x 1 = 4− (−1) 3 − 1 = 5 2 (b) The mid-point of a line joining the points ( x 1 , y 1 ) and ( x 2 , y 2 ) is given by: ( x 1 + x 2 2 , y 1 + y 2 2 ) Hence mid-point of AB = ( 1 + 3 2 , − 1 + 4 2 ) = ( 2, 3 2 ) (c) The product of the gradients of perpendicular lines is −1. Hence m ( 5 2 ) = −1 Giving m = − 2 5 Equation of straight line L having gradient − 2 5 and passing through the point ( 2, 3 2 ) is: y − 3 2 = − 2 5 x − 2 > > >  TIP In many questions you would be advised to take the time to plot the points given on a quick sketch graph. This is a simple question so it is not really worth the time. In questions involving more points, you should mark the points and lines on a graph. TAKE NOTE We often re-write equations involving fractions into a form that does not contain fractions (i.e. they only contain whole numbers). Choose the smallest number that the denominators both go into and then multiply the whole equation by this number thus removing the fractions. 22 Find the coordinates of the point of intersection of the following two lines: 7 y = 5 x − 27 4 y = 3 x − 16 23 Explain why the two lines having equations y − 3 x + 4 = 0 and 4 y  − 12 x  + 1 = 0 do not intersect. 24 The line AB has equation 4 x + y = 1 The line with equation 3 x + 2 y = 7 intersects the line AB at point A . Find the coordinates of A . 2 Coordinate geometry 138