PROSZĘ NA DZISIAJ!! DAJĘ NAJ!!
Odcinek AB o końcach A(-5,5) i B(5,0) podzielono na pięć odcinków równej długości. Oblicz współrzędne punktów podziału.
" Life is not a problem to be solved but a reality to be experienced! "
© Copyright 2013 - 2024 KUDO.TIPS - All rights reserved.
-->
AB = [ 5 - (-5); 0 - 5] = [ 10 ; - 5]
Niech
A1 = (x1; y1), A2 = (x2 ; y2), A3 = (x3; y3), A4 = (x4; y4)
będą tymi punktami podziału odcinka AB.
Mamy
-->
AA1 = (1/5)*{ 10 ; - 5] = [ 2 ; - 1]
oraz
-->
AA1 = [ x1 - (-5); y1 - 5] = [ x1 + 5; y1 - 5]
zatem
x1 + 5 = 2 i y1 - 5 = - 1
x1 = -3 i y1 = 4
A1 = ( -3; 4)
===========
-->
A A2 = (2/5)*[ 10 ; - 5] = [ 4; - 2]
oraz
-->
A A2 = [ x2 + 5; y2 - 5]
czyli
x2 + 5 = 4 i y2 - 5 = - 2
x2 = -1 i y2 = 3
A2 = ( -1 ; 3)
=============
-->
A A3 = (3/5) *[ 10 [ - 5] = [ 6; - 3 ]
oraz
-->
A A3 = [ x3 + 5; y3 - 5 ]
czyli
x3 + 5 = 6 i y3 - 5 = - 3
x3 = 1 i y3 = 2
A3 = ( 1 ; 2)
===============
-->
A A4 = (4/5) * [ 10 ; - 5] = [ 8; - 4]
oraz
-->
A A4 = [ x4 + 5; y4 - 5 ]
czyli
x4 + 5 = 8 i y4 - 5 = - 4
x4 = 3 i y4 = 1
A4 = ( 3; 1 )
==============
Odp. A1 = (-3; 4), A2 = ( -1 ; 3), A3 = ( 1; 2), A4 = (3; 1)
=======================================================