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Maths 4 Scotland Higher The following questions are on The Straight Line Non-calculator questions will be indicated You will need a pencil, paper, ruler and rubber. Click to continue

Maths 4 Scotland Higher Find the equation of the line which passes through the point (-1, 3) and is perpendicular to the line with equation Find gradient of given line: Find gradient of perpendicular: Find equation: Hint Previous Quit Next

Maths 4 Scotland Higher Find the equation of the straight line which is parallel to the line with equation and which passes through the point (2, – 1). Find gradient of given line: Gradient of parallel line is same: Find equation: Hint Previous Quit Next

Maths 4 Scotland Higher Find the size of the angle a° that the line joining the points A(0, -1) and B(3 3, 2) makes with the positive direction of the x-axis. Find gradient of the line: Use table of exact values Hint Previous Quit Table of exact values Quit Next

Maths 4 Scotland Higher A and B are the points (– 3, – 1) and (5, 5). Find the equation of a) the line AB. b) the perpendicular bisector of AB Find gradient of the AB: Find equation of AB Find mid-point of AB Gradient of AB (perp): Use gradient and mid-point to obtain perpendicular bisector AB Hint Previous Quit Next

Maths 4 Scotland The line AB makes an angle of Higher radians with the y-axis, as shown in the diagram. Find the exact value of the gradient of AB. (x and y axes are perpendicular) Find angle between AB and x-axis: Use table of exact values Hint Previous Quit Table of exact values Quit Next

Maths 4 Scotland Higher A triangle ABC has vertices A(4, 3), B(6, 1) and C(– 2, – 3) as shown in the diagram. Find the equation of AM, the median from A. Find mid-point of BC: Find gradient of median AM Find equation of median AM Hint Previous Quit Next

Maths 4 Scotland Higher P(– 4, 5), Q(– 2, – 2) and R(4, 1) are the vertices of triangle PQR as shown in the diagram. Find the equation of PS, the altitude from P. Find gradient of QR: Find gradient of PS (perpendicular to QR) Find equation of altitude PS Hint Previous Quit Next

Maths 4 Scotland Higher The lines and make angles of a and b with the positive direction of the x-axis, as shown in the diagram. a) Find the values of a and b b) Hence find the acute angle between the two given lines. Find gradient of Find a° Find gradient of Find b° Use angle sum triangle = 180° Find supplement of b Angle between two lines 72° Hint Previous Quit Next

Maths 4 Scotland Triangle ABC has vertices A(– 1, 6), B(– 3, – 2) and C(5, 2) Find: a) the equation of the line p, the median from C of triangle ABC. b) the equation of the line q, the perpendicular bisector of BC. c) the co-ordinates of the point of intersection of the lines p and q. Find mid-point of AB (-2, 2) Find gradient of p Higher Find equation of p Find mid-point of BC (1, 0) Find gradient of BC Find gradient of q Find equation of q Solve p and q simultaneously for intersection (0, 2) Hint Previous Quit Next

Maths 4 Scotland Triangle ABC has vertices A(2, 2), B(12, 2) and C(8, 6). a) Write down the equation of l 1, the perpendicular bisector of AB b) Find the equation of l 2, the perpendicular bisector of AC. c) Find the point of intersection of lines l 1 and l 2 d) Hence find the equation of the circle passing through A, B and C. Perpendicular bisector AB Mid-point AB Find mid-point AC (5, 4) Find gradient of AC Equ. of perp. bisector AC Gradient AC perp. Point of intersection Higher (7, 1) This is the centre of circle Find radius (intersection to A) Equation of circle: Previous Hint Quit Next

Maths 4 Scotland Higher A triangle ABC has vertices A(– 4, 1), B(12, 3) and C(7, – 7). a) Find the equation of the median CM. b) Find the equation of the altitude AD. c) Find the co-ordinates of the point of intersection of CM and AD Mid-point AB Gradient CM (median) Equation of median CM Gradient BC Gradient of perpendicular AD Equation of AD Solve simultaneously for point of intersection (6, -4) Hint Previous Quit Next

Maths 4 Scotland A triangle ABC has vertices A(– 3, – 3), B(– 1, 1) and C(7, – 3). a) Show that the triangle ABC is right angled at B. b) The medians AD and BE intersect at M. i) Find the equations of AD and BE. ii) Hence find the co-ordinates of M. Gradient AB Gradient BC Product of gradients Mid-point BC Mid-point AC Higher Hence AB is perpendicular to BC, so B = 90° Gradient of median AD Gradient of median BE Equation AD Solve simultaneously for M, point of intersection Hint Previous Quit Next

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Maths 4 Scotland Higher Table of exact values 30° 45° sin cos tan Return 1 60°