a
Middle
School
Grade 6
Grade 7
Grade 8
Grade 9
Ressource
Out Middle
High
School
Grade 10
Grade 11
Grade 11 - STMG
Grade 12 - STMG
Grade 12
Grade 12 - Comp.
Grade 12 - Exp.
Ressource
Out High
4
3
2
1
Outside the high school program
/ scalar product in space
3 exercises (100% corrected)
a
Median formula
(4 exercices)
1.
Me
dian
formula
E.6807
Reminders
:
Let
A
and
B
b
e
t
w
o
p
oin
ts
on
the
plane
and
I
the
midp
oin
t
of
the
segmen
t
[
AB
]
.
F
or
an
y
p
oin
t
M
on
the
plane,
w
e
ha
v
e
the
relationship
:
AM
2
+
B
M
2
=
1
2
·
AB
2
+
2
·
M
I
2
Consider
the
plane
equipp
ed
with
an
orthonormal
co
ordinate
system
O
;
I
;
J
and
the
three
p
oin
ts
A
,
B
,
and
C
with
re-
sp
ectiv
e
co
ordinates
:
A
(
−
2
;
−
3
)
;
B
(
−
1
;
2
)
;
C
(
3
;
1
)
1
Determine
the
measures
AB
,
AC
,
and
B
C
.
2
a
Let
I
b
e
the
midp
oin
t
of
segmen
t
[
AB
]
.
Determine
the
measure
of
the
median
in
triangle
AB
C
originating
at
v
ertex
C
.
b
Let
J
b
e
the
midp
oin
t
of
segmen
t
[
AC
]
.
Determine
the
length
of
the
median
in
triangle
AB
C
originating
at
v
ertex
B
.
E.2663
Consider
a
triangle
AB
C
righ
t-
angled
at
A
with
the
follo
wing
measures
:
AB
=
6
;
AC
=
3
Let
I
b
e
the
midp
oin
t
of
segmen
t
[
AB
]
and
J
the
midp
oin
t
of
[
I
C
]
.
W
e
are
in
terested
in
the
set
E
of
p
oin
ts
M
v
erifying
the
rela-
tion
:
M
A
2
+
M
B
2
+2
·
M
C
2
=
72
1
er
metho
d
:
1
Sho
w
that
all
p
oin
ts
M
v
erify
the
relation
:
M
A
2
+
M
B
2
+
2
×
M
C
2
=
4
·
M
J
2
+
J
A
2
+
J
B
2
+
2
×
J
C
2
2
Using
the
median
theorem
t
wice,
demonstrate
the
follo
w-
ing
relationship
:
M
∈
E
⇐
⇒
4
×
M
J
2
+
AB
2
2
+
I
C
2
=
72
3
Deduce
the
nature
of
the
set
E
.
2
ème
metho
d
:
The
plane
is
giv
en
the
reference
frame
A
;
1
6
·
−
−
→
AB
;
1
3
·
−
→
AC
1
Determine
the
co
ordinates
of
p
oin
ts
A
,
B
,
C
in
this
frame.
2
Noting
(
x
;
y
)
the
co
ordinates
of
p
oin
t
M
,
determine
an
equation
of
E
in
this
reference
frame.
3
Deduce
the
nature
of
the
set
E
.
E.2609
Consider
the
plane
pro
vided
with
a
reference
frame
(
O
;
I
;
J
)
orthonormal
and
the
follo
wing
t
w
o
p
oin
ts
in
the
plane
:
A
(
−
3
;
2
)
;
B
(
3
;
−
6
)
1
W
e
will
denote
b
y
M
the
p
oin
t
with
co
ordinates
(
x
;
y
)
:
a
Determine
the
co
ordinates
of
p
oin
t
I
middle
of
[
AB
]
.
b
Determine
the
co
ordinates
of
the
v
ectors
−
−
→
I
M
and
−
−
→
AB
.
c
Determine
the
length
AB
.
2
a
Determine
the
Cartesian
equation
of
the
set
of
p
oin
ts
v
erifying
the
relation
:
M
A
2
−
M
B
2
=
40
b
Giv
e
the
nature
and
c
haracteristic
elemen
ts
of
the
p
oin
ts
M
v
erifying
this
relation.
3
a
Determine
the
equation
of
the
set
of
p
oin
ts
v
erifying
the
relation
:
−
−
→
M
A
·
−
−
→
M
B
=
34
b
Giv
e
the
nature
and
c
haracteristic
elemen
ts
of
the
p
oin
ts
M
v
erifying
this
relationship.
4
a
Determine
the
equation
of
the
set
of
p
oin
ts
v
erifying
the
relation
:
M
A
2
+
M
B
2
=
150
b
Giv
e
the
nature
and
c
haracteristic
elemen
ts
of
the
p
oin
ts
M
v
erifying
this
relation.
h
ttps:/
/c
hingmath.fr
chapExoCorrec/6807
sacados/6807
chapExoCorrec/2663
sacados/2663
chapExoCorrec/2609
sacados/2609
ChingMath
by ChingLab
©
Middle School
Grade 6
Grade 7
Grade 8
Grade 9
High School
Grade 10
Grade 11
Grade 12
Grade 12 opt. Complémentaire
Grade 12 opt. Experte
Various
Contact me
F.A.Q
Other website
ChingWeb