1. Higher Maths The Straight Line Strategies Click to start
Higher Maths
Strategies
The Straight Line
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2. 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.
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3. 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
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4. 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
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5. 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
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Table of exact values

6. 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
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7. 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
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Table of exact values

8. 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
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9. 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
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10. 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
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11. (-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)
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12. (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:
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13. (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
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14. 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
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15. You have completed all 12 questions in this presentation
Maths4Scotland Higher
You have completed all 12 questions in this presentation
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16. 30° 45° 60° sin cos tan 1 Table of exact values Maths4Scotland Higher
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