the internal division and the external divison of a line...

40
The internal division and the external divison of a line segment X ·ü x (The internal division and the external divison of a line segment) Min Eun Gi : https://www.facebook.com/mineungimath

Upload: others

Post on 21-Mar-2020

1 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

선분의내분점과외분점(The internal division and the external divison of a line segment)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 2: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 3: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 4: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 5: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 6: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 7: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 8: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 9: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 10: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 11: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 12: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 13: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 14: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 15: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 16: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 17: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 18: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 19: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Start

Min Eun Gi : https://www.facebook.com/mineungimath

Page 20: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Home

Min Eun Gi : https://www.facebook.com/mineungimath

Page 21: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 22: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의

두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 23: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여

AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 24: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를

m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 25: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 26: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점

P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 27: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)

(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 28: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점

P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 29: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)

(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 30: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 31: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의

두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 32: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여

AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 33: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를

m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 34: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 35: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점

P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 36: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)

(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 37: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점

P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 38: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)

(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 39: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath

Page 40: The internal division and the external divison of a line ...min7014.iptime.org/math/2015030801.pdf · The internal division and the external divison of a line segment —X·— ü

The internal division and the external divison of a line segment

Theorem

수직선위의두점 A(x1), B(x2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n

)(2) 외분하는점 P2

(mx2 − nx1

m− n

)(m 6= n)

Theorem

좌표평면위의두점 A(x1, y1), B(x2, y2)에대하여 AB를 m : n으로

(1) 내분하는점 P1

(mx2 + nx1

m + n,

my2 + ny1

m + n

)(2) 외분하는점 P2

(mx2 + nx1

m− n,

my2 + ny1

m− n

)(m 6= n)

Min Eun Gi : https://www.facebook.com/mineungimath