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# The Midpoint Formula ÙØ§ÙÙÙ Ø¥Ø­Ø¯Ø§Ø«Ù ÙÙØªØµÙ ÙØ·Ø¹Ø© ÙØ³ØªÙÙÙØ© - PowerPoint PPT Presentation

The Midpoint Formula قانون إحداثي منتصف قطعة مستقيمة. The Midpoint Formula. B ( x 2 , y 2 ). •. M. A ( x 1 , y 1 ). •. 2. -2. 4. -4. ( -1 , 1 ). 2. -2. - 1 , 1. A ( - 4 , 4 ). A = ?. Note :. A = 2M – B. If one endpoint is given &amp; M is given.

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Presentation Transcript

The Midpoint Formula

قانون إحداثي منتصف قطعة مستقيمة

The Midpoint Formula

B ( x2 , y2 )

M

A ( x1 , y1 )

2

-2

4

-4

( -1 , 1 )

2

-2

-1 , 1

A ( - 4 , 4 )

A = ?

Note :

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

∴ A = ( - 4 , 4 )

OR

B = 2M – A

M : the center of the circle

A , B can be the endpoints of a diameter of a circle

Note :

A

B = 2M – A

If one endpoint

is given & M is given

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 )

Zayed althani school

The Distance Formula

The Midpoint Formula

Q 1

Math department

Find the coordinates of the center of the circle

أوجد إحداثيات مركز الدائرة

𝒚

A =

4

B =

( Apply the formula )

طبق القانون

M =

3

A

2

M

1

A =

𝒙

B =

B

-5

-4

-2

-3

-1

4

5

1

2

3

C =

( Apply the formula )

طبق القوانين

A

-1

Q 2

M =

-2

M is the midpoint of AC

A C =

Find M

M

-3

Prove that : AC = 2×BM

B M =

-4

C

B

Worksheet ( 2 )

Zayed althani school

The Midpoint Formula

Q 1

Math department

Draw the diagonals of the parallelogram in the figure

أارسم اقطار متوازي الأضلاع في الشكل

𝒚

Find the midpoint of AC =

4

D (-1 , 3)

C (6 , 3)

3

Find the midpoint of BD =

2

1

𝒙

Q 2

-5

-4

-2

-3

-1

4

5

1

2

3

Given M ( 1 , - 3 ) is the midpoint of XY

Where : X ( 4 , -2 ) find the coordinates of Y

-1

B(5 ,-1)

A (-2 ,-1)

-2

-3

Draw XY & locate M

ارسم هذه القطعة المستقيمة وبين نقطة المنتصف

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