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The Straight Line The following questions are on Maths4Scotland 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

Maths4Scotland 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 Quit Next

Maths4Scotland 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 Quit Next

Find the size of the angle a° that the line joining the Maths4Scotland 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 Use table of exact values Hint Previous Quit Quit Next Table of exact values

A and B are the points (–3, –1) and (5, 5). Find the equation of Maths4Scotland 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 Quit Next

The line AB makes an angle of radians with the Maths4Scotland Higher The line AB makes an angle of radians with the y-axis, as shown in the diagram. Find the exact value of the gradient of AB. Find angle between AB and x-axis: (x and y axes are perpendicular) Use Use table of exact values Hint Previous Quit Quit Next Table of exact values

A triangle ABC has vertices A(4, 3), B(6, 1) Maths4Scotland 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 Quit Next

P(–4, 5), Q(–2, –2) and R(4, 1) are the vertices Maths4Scotland 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 Quit Next

72° The lines and make angles of a and b with the positive Maths4Scotland 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° Find supplement of b Use angle sum triangle = 180° 72° Hint Angle between two lines Previous Quit Quit Next

(-2, 2) (1, 0) (0, 2) Maths4Scotland Higher 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 Find equation of p Find mid-point of BC (1, 0) Find gradient of BC Find gradient of q Find equation of q Hint Solve p and q simultaneously for intersection (0, 2) Previous Quit Quit Next

(5, 4) (7, 1) Maths4Scotland Higher Triangle ABC has vertices A(2, 2), B(12, 2) and C(8, 6). a) Write down the equation of l1, the perpendicular bisector of AB b) Find the equation of l2, the perpendicular bisector of AC. c) Find the point of intersection of lines l1 and l2 d) Hence find the equation of the circle passing through A, B and C. Mid-point AB Perpendicular bisector AB (5, 4) Find mid-point AC Find gradient of AC Gradient AC perp. Equ. of perp. bisector AC Point of intersection (7, 1) This is the centre of circle Find radius (intersection to A) Hint Equation of circle: Previous Quit Quit Next

(6, -4) Maths4Scotland 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 (6, -4) Hint Solve simultaneously for point of intersection Previous Quit Quit Next

A triangle ABC has vertices A(–3, –3), B(–1, 1) and C(7,–3). Maths4Scotland Higher 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 Hence AB is perpendicular to BC, so B = 90° Mid-point BC Gradient of median AD Equation AD Mid-point AC Gradient of median BE Equation AD Hint Solve simultaneously for M, point of intersection Previous Quit Quit Next

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30° 45° 60° sin cos tan 1 Table of exact values Maths4Scotland Higher Return