Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Higher Mathematics > 1. Straight Line > Flashcards

1. Straight Line Flashcards

1
Q

2 forms of straight line equation

A

y = mx + c
(m is gradient, c is y intercept)

ax + by + c = 0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Gradient equation

A

m = y2 - y1 / x2 - x1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

Gradient of line sloping up from left to right

A

+ive

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

Gradient of line sloping down from left to right

A

-ive

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

Gradient of a horizontal line

A

0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

Gradient of a vertical line

A

Undefined

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

Lines with the same gradient are ______

A

parallel

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

Gradient of the line joining A (6,3) and B (3,8)

A

-5 / 3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

Given the points C (2,p) and D (10,7) have a gradient of 1/4, find the value of p

A

p = 5

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

Requirements for collinearity

A

3 or more points on a straight line

Same gradient

Share a common point

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

3 or more points on a straight line

Same gradient

Share a common point

A

Requirements for collinearinity

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Method for proving collinearity of A, B, and C

A
  1. Gradient AB
  2. Gradient BC
  3. Statement
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Collinearity statement

A

Since mAB = mBC and share common point B, the points A, B and C are collinear

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

Are A (2,6), B (-1, 3) and C (3,8) collinear?

A

Not collinear as mAB ≠ mBC

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

tan0 =

A

Gradient, y2 - y1 / x2 - x1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What can be found with tan0 = m

A

If gradient is known, angle can be found

If angle is known, gradient can be found

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

If gradient is known, angle can be found

If angle is known, gradient can be found

A

m = tan0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

Angle from triangle of straight line e =

A

Angle the straight line makes with x axis

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

Negative on bottom and top of fraction

A

Becomes positive as it cancels out

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

Calculate the size of the angle of the line joining P (3,9) and Q (-2, 1)

A

Gradient = 8 / 5

Angle = 57.99 °

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

How to find the distance between two known points

A

By constructing a right angle triangle

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

Distance formula

A
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

Find the distance between A (5,7) and B (-8, 2)

A

13.93

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

Rearrange 3x -2y = -7 and find a, b, and c

A

3x - 2y + 7 = 0

a = 3
b = -2
c = 7

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

rearrange y = -5x + 9 and find a b and c

A

5x + y - 9 = 0

a = 5, b = 1, c = -9

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

Rearrange to the general equation and find the values of a, b, and c:

y - 2 = 3/4 (x + 5)

A

-3x + 4y - 23 = 0

a = -3, b = 4, c = 23

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

find the gradient and y intercept:

4x + 2y + 10 = 0

A

m = -2, c = -5

28
Q

find the gradient and y intercept:

3x -5y + 1 = 0

A

m = 3/5

c = 1/5

29
Q

find the gradient and y intercept:

4 - x - 3y = 0

A

m = -1/3

c = 4/3

30
Q

rearrange y = 1/4x - 1/3 into the form ax + by + c = 0

A

-3x + 12y + 4 =0

31
Q

Equation for SL if we know one point and its gradient

A

y - b = m (x - a)

32
Q

when to use y - b = m (x - a)

A

when you know one point and the gradient

33
Q

components of straight line

A

Gradient

Point

Equation

34
Q

Find the equation of the line passing through (4, 7) with the gradient of 2

A

y = 2x - 1

35
Q

Find the equation of the line that passes through the point (4, 3) and (7, 15)

A

m = 4
a = 4
b = 3

y = 4x - 13

36
Q

Perpendicular

A

Two lines that are at right angles to each other

37
Q

Two lines that are at right angles to each other

A

Perpendicular

38
Q

Rule for gradients of perpendicular lines

A

m1 x m2 = -1

To find a perpendicular gradient, flip the original gradient upside down and change the sign.

39
Q

Find the perpendicular gradient of:

1/2

-5/3

0.25

1

-6

A

-2

3/5

-4

-1

1/6

0

40
Q

Method for proving perpendicularity

A
  1. Find gradient of equation/line one
  2. Find gradient of equation/line two
  3. Statement - m1 x m2 = -1
41
Q

Prove the lines x + 3y + 6 = 0 and y = 3x - 1 are perpendicular

A

Gradient 1 = -1/3

Gradient 2 = 3/1

Since m1 x m2 = -1, the lines are perpendicular

42
Q

Find the equation of the line through the points (-3, 1) which is perpendicular to the line y = 2 - 4x

A

Gradient of y = 2 - 4x = -4

y = 1/4x + 7/4

43
Q

Midpoint

A

Point exactly half way between two points

44
Q

Point exactly half way between two points

A

midpoint

45
Q

Midpoint equation

A

( x1 + x2 / 2, y1 + y2 / 2)

46
Q

( x1 + x2 / 2, y1 + y2 / 2)

A

Midpoint

47
Q

Find the midpoint of A (2, 8) and B (4, 6)

A

(3, 7)

48
Q

Find the midpoint of (5, -7) and D (6, 4)

A

(5.5, -1.5)

49
Q

Median

A

The line from a vertex to the midpoint of the opposite side. A triangle has 3 medians.

Vertex = corner of triangle

50
Q

Where do 3 medians meet

A

Centroid

51
Q

Find the equation of the median from L in the triangle with the vertices K (3, 7), L (-1, -5), and M (7, 3)

A

Mid point KM = (5, 5)

Gradient of L = 5/3

y = 5/3x - 10/3

52
Q

Concurrent

A

Any number of lines that all pass through the same point

53
Q

Altitude

A

A line that goes from a vertex to the opposite side and meets at a right angle

54
Q

A line that goes from a vertex to the opposite side and meets at a right angle

A

Altitude

55
Q

How many altitudes does a triangle have

A

3

56
Q

What meet at the orthocentre

A

Altitudes

57
Q

Method for finding equation of altitude

A

Find gradient of line perpendicular to altitude

Find gradient of altitude

Sub into y = m (x - a)

58
Q

A is the point (2, -4), B (3, 1), C (-5, 0). Find the equation of the altitude from B

A

Gradient AC 4/-7

y = 7/4x - 17/4

59
Q

Perpendicular bisector

A

A line that cuts another line in half, at right angles

60
Q

How many perp. bisectors does a triangle have

A

3

61
Q

What do perp. bisectors meet at

A

The circumcentre

62
Q

Method for finding equation of perp. bisectors

A
  1. find midpoint of line perpendicular to perpendicular bisector
  2. Find gradient of line perpendicular to perpendicular bisector
  3. Find gradient of perpendicular bisector
  4. Sub known data into y = m (x - a)
63
Q

Find perpendicular bisector of the line joining A (-4, 6) and C (-2, -2)

A

Mid point AC (-3, 2)

Gradient AC -4

Perpendicular gradient 1/4

y = 1/4x + 11/4

64
Q

What do we use to find the point of intersection

A

Simultaneous equations

65
Q

Method for simultaneous equations in points of intersection

A

Rearrange at least one of the equations into the form “x=“ or “y=“ and substitute into each other

OR

Write the equation in the form ax + by + c = 0 and cancel the x or y term

66
Q

Find the point of intersection of the lines y = x + 1 and 4y + 2x = 16

A

(2, 3)

67
Q

Find the point of intersection of 3x + 5y - 23 = 0 and 5x + 2y - 13 = 0

A

(1, 4)

Higher Mathematics (7 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions