higher maths
DESCRIPTION
www.maths4scotland.co.uk. Higher Maths. Strategies. The Straight Line. Click to start. Maths4Scotland Higher. The following questions are on. The Straight Line. Non-calculator questions will be indicated. - PowerPoint PPT PresentationTRANSCRIPT
Higher Maths
Strategies
www.maths4scotland.co.uk
Click to start
The Straight Line
Maths4Scotland Higher
The Straight Line
The following questions are on
Non-calculator questions will be indicated
Click to continue
You will need a pencil, paper, ruler and rubber.
Maths4Scotland Higher
Hint
Previous NextQuitQuit
Find the equation of the line which passes through the point (-1, 3)
and is perpendicular to the line with equation 4 1 0x y
Find gradient of given line: 4 1 0 4 1 4x y y x m
Find gradient of perpendicular:1
4m
Find equation:1 3
1 4( 3) 1 4 124 ( 1)
yx y x y
x
4 13 0y x
Maths4Scotland Higher
Hint
Previous NextQuitQuit
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:2
3m
Find equation: 2 ( 1)2 4 3 3
3 2
yx y
x
3 2 1y x
2 3 5x y
2 2
3 33 2 5 5y x y x m
Maths4Scotland Higher
Hint
Previous NextQuitQuitTable of exact values
Find gradient of the line:
1tan
3
Use table of exact values1 1
tan 303
2 ( 1) 3 1
3 3 0 3 3 3m
Use tanm
Find the size of the angle a° that the line joining the
points A(0, -1) and B(33, 2) makes with the
positive direction of the x-axis.
Maths4Scotland Higher
Hint
Previous NextQuitQuit
A and B are the points (–3, –1) and (5, 5).Find the equation ofa) the line AB.
b) the perpendicular bisector of AB
Find gradient of the AB: 4 3 5y x
Find mid-point of AB 1, 3
3
4m Find equation of AB
Gradient of AB (perp):4
3m
Use gradient and mid-point to obtain perpendicular bisector AB
3 4 13y x
Maths4Scotland Higher
Hint
Previous NextQuitQuitTable of exact values
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:2 3 6
Use table of exact values
3
Use tanm tan6
m
1
3m
(x and y axes are perpendicular)
Maths4Scotland Higher
Hint
Previous NextQuitQuit
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: (2, 1)
Find equation of median AM
Find gradient of median AM 2m
2 5y x
Maths4Scotland Higher
Hint
Previous NextQuitQuit
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:1
2m
Find equation of altitude PS
Find gradient of PS (perpendicular to QR) 2m
2 3 0y x
Maths4Scotland Higher
Hint
Previous NextQuitQuit
The lines and makeangles of a and b with the positivedirection of the x-axis, as shown in the diagram.a) Find the values of a and bb) Hence find the acute angle
between the two given lines.
2m
Find supplement of b 180 135 45
2 4y x 13x y
Find gradient of 2 4y x
Find gradient of 13x y 1m
Find a° tan 2 63a a
Find b° tan 1 135b b
Angle between two lines
Use angle sum triangle = 180°
72°
Maths4Scotland Higher
Hint
Previous NextQuitQuit
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
Find equation of p 2y
Find gradient of p(-2, 2)
Find mid-point of BC (1, 0) Find gradient of BC1
2m
0m
Find gradient of q 2m Find equation of q 2 2y x
Solve p and q simultaneously for intersection (0, 2)
Maths4Scotland Higher
Hint
Previous NextQuitQuit
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.
7, 2Mid-point AB
Find mid-point AC (5, 4) Find gradient of AC2
3m
Equ. of perp. bisector AC
26r
Gradient AC perp.3
2m 2 3 23y x
Point of intersection (7, 1) This is the centre of circle
Find radius (intersection to A)
Equation of circle: 2 27 1 26x y
7x Perpendicular bisector AB
Maths4Scotland Higher
Hint
Previous NextQuitQuit
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
4, 2Mid-point AB
Equation of median CM
Gradient of perpendicular ADGradient BC 2m1
2m
Equation of AD
3mGradient CM (median)
3 14y x
Solve simultaneously for point of intersection (6, -4)
2 2 0y x
Maths4Scotland Higher
Hint
Previous NextQuitQuit
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. 2mGradient AB
Product of gradients
Gradient of median ADMid-point BC 3, 11
3m Equation AD
1
2mGradient BC
12 1
2
Solve simultaneously for M, point of intersection
3 6 0y x
Hence AB is perpendicular to BC, so B = 90°
Gradient of median BEMid-point AC 2, 34
3m Equation AD 3 4 1 0y x
51,
3
Maths4Scotland Higher
Previous QuitQuit
You have completed all 12 questions in this presentation
Back to start
Maths4Scotland Higher
Return
30° 45° 60°
sin
cos
tan 1
6
4
3
1
2
1
23
2
3
2
1
21
21
3 3
Table of exact values