### B - math-secrets

‫‪The Midpoint‬‬
‫‪Formula‬‬
‫قانون إحداثي منتصف‬
‫قطعة مستقيمة‬
The Midpoint Formula
B ( x2 , y2 )
•
M
A ( x1 , y1 )
-4
2
-2
4 -2
2
-1 , 1
( -1•, 1 )
Note :
A ( A- 4
= ,?4 )
A = 2M – B
If one endpoint
is given & M is
given
A = 2 ( -1 , 1 ) – ( 2 , -2 )
Then :
M
A = ( -2 , 2 ) – ( 2 , -2 )
A = ( -2 – 2 , 2 – - 2 )
A = 2M – B
B
OR
B = 2M – A
M : the center
of the circle
A , B can be the endpoints of
a diameter of a circle
∴ A=(-4, 4)
Note :
If one endpoint
is given & M is
given
A
B = 2M – A
B = 2 ( -1 , 1 ) – ( - 4 , 4 )
Then :
M
B = ( -2 , 2 ) – ( - 4 , 4 )
B = ( -2 – - 4 , 2 – 4 )
A = 2M – B
∴ B=(2,–2 )
OR
B
B(=2?, -2 )
B = 2M – A
M : the point
of
intersection
of the two
diagonals
A , B can be the endpoints of
a diagonal of a parallelogram
Worksheet ( 1 )
Q1
Find the coordinates of the center of the circle
‫أوجد إحداثيات مركز الدائرة‬
A=
B=
M=
-5
-4
-3
( Apply the formula )
‫طبق القوانين‬
-2
A
x1  x2 y1  y2
M (
,
)
2
2
-1
M
1
2
5

M is the midpoint of AC
Find
M
Prove that : AC = 2×BM
-4
B
3B 4
Q2
-1
-3 M
BM=
AC

BM
The Midpoint Formula
-2
AC=
x2  x1 2   y2  y1 2
2
1
M=
now

3
A=
C=
d
4
( Apply the formula )
‫طبق القانون‬
A
B=
The Distance Formula
C
Zayed althani school
Math department
Worksheet ( 2 )
Q1
The Midpoint Formula
x1  x2 y1  y2
M (
,
)
2
2
Draw the diagonals of the parallelogram in the figure
‫أارسم اقطار متوازي األضالع في الشكل‬

Find the midpoint of AC =
4
3
Find the midpoint of BD =
2
1
Q2
-5
-4
-3
-2
-1
1
Given M ( 1 , - 3 ) is
the midpoint of XY
-1
Where : X ( 4 , -2 )
find the coordinates
of Y
-2
Draw XY & locate M
-3
‫ارسم هذه القطعة المستقيمة وبين‬
‫نقطة المنتصف‬
-4
2
3
4
5

Zayed althani school
Math department