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Mathematics AI IB , 11th grade coordinate geometry & lines
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There are some notes about Math in the IB program which help you to understand more the exercises about geometry and lines.
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Exercise 4A (Midpoint)1 .
. A (1 , 4)
3 B) 3 , - -
4) 11
9) A (2 ,
1) BIr ,
3 . 5) find coordinates of C
(( , ) ( 1 0
↑
M = =
,
M
(35) (1 7 1 .
= =
,
. .
(+ z)
M = = (0 , 2)
,
b) Al 1 , 5 , - 4 2) -
.
B (7 , 8 5 -11)
,
.
C =
(0 ,
2)
M=
(5 ,
)
=
(3, 6 75, -7 .
4
. a .
16 7 , ,
0)
2 b .
(6 , 7 , 4)
A) -
2
,
1) B (2 ,
-
4) .
2 A(6 , 7
,
4) 010 ,
0, 0
M= (3 3 5 2) ,
.
,
M=
(z , ) = 10;
Exercise 4B (Distance ( .
A (1 , 7)
1 4 .
c =
T .
d
·
a) A (4 , -3) BC 1 5 -
.
,
5) C = T -
6 71,
2 =
21 08
,
d =
, 4)2
-
+ 15 -
7 39)2 d
d = -50
25 + 64 .
d =
( z -
1) + (1 -
7)2
d =
9 78 d = 6 . 71
.
6) All ,
-2
,
10) B(-4 , 0 3) ,
B( -
2, 1)
d = 1 2
+ 20 + 2)2 + (3- 10)3
D(3 , 6)
d= 5 + 4+ 49 S . E(X 6) ,
d =
8 83 (M
I
.
.
2 PQ =
2km
P(X , 7) ② (3 , 5)
I
G(1 , 3) F
z = ((3 x)2 + -
(5 -
7)2
2 = (3 -
X) + ( -
2) G (1 , 3) E(X , 6)
z 3 2 H (4 4)
X X 3
= -
=
-
,
Et
2 = 1 -
X # = m(4)
2
.
3 A(-4 6) ,
B16 , 2) ((-8 , -4) ↳ n 5 .
B
E2
ABd =
(6 + 4)2 + (2 - 6)2'6 ·
= M+ 16 a) ((26 -
2032 + (31 -
25)2 + (12 11)2 -
AB =
6 =
8 54.
A (d = v( -
8 + 4)2 + ( 4 - -
6/2
7 = 16 + 100
I
b) radar
The will be
C
Num = able to detect one
AC "
BCd = ( 8
-
-
6)2 + ( 4 -
212 but not both .
-
4 + 36
AB2 + Acc =
BC
:
=
32 .
, Exercise 4C (Gradient of a line) zero gradient
Indicates the steepness line and direction
of the
NegativeGradient
. Positive
1&
gradient
.
Horizontal - Gradient is zero
vertical = rise
horizontal
b
= run
. vertical -
> undefined gradient
.a
2 . ACC 3) B(-1 4) , ,
m
A
= = :
b Al-11 2) B(2 7)
.
, ,
m
= =
3
C
. Al-1 3 2) 3)
2
B(G =
-0 m = 0 3-2 2 . .
,
. . .
,
1 .
2 + 1 . 3
. Stair
3 1: 12/25 =
0 48.
.
6 -
3 is the steeper because for be down
(1) the
Stair 2 : 10/20 = 0 .
5 skier couldn't go horizontally .
1
Stair 3 : 15/18 = 0 . 83
7 A (90 , 10) 16490 n) ,
a) stair 3 has the greatest gradient. 3 35
0
10
=
6) stair 1 has the least gradient
=
03
4 9) . (3) AL0 0) BC-5
,6
, . 35 400
0 .
= -10
⑧i -
6 m = 1 = - 1
,
2 140 = n 10
-
-
5 n = 150 meters
5
rise 4
-
3
2-
1
11(x)
run
I
· I
I' 123 4
&
b) AC-1 2) B73 -5) , ,
↳
· 2-
M=
=3
1 -
* 11 I 11 *
in 3
O
- -
2
-
1 1 .
1 23
2
-
-
-
3
4-
-
5.
-
·
Sp
5
. a)
2 = 1=
m = 0
b)
55 ==
m
=
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