KESKEN, YHDENSUUNTAISPROJEKTIO, ORTOGONAALIPROJEKTIOT

Sketch 1

In the following sketch you see a fixed point S and a dragable point x. In some positions you also see a point x'.

a) What is the image u' of the fixed point u; give its coordinates.

b) Furthermore, what is the image of the fixed point v?

c) Give practical examples (explanations) of what the picture is about.

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Sketch 2

In the following sketch you see a dragable point S and a fixed point x. In some positions you also see a point x'.

a)

b)

c)

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$LSx Line($S,$x)[white,hidden]; $LperpLrefl Perpendicular($Lrefl,$x)[blue,hidden]; $Pprojx Intersect($Lrefl,$LperpLrefl)[blue,traced,hidden]; $SxPprojx Segment($Pprojx,$x)[red]; $SxPctr Segment($Pctr,$x)[red,thick]; $Kx Coordinates($x,$coord,5,50,'x = ')[red]; $KQ Coordinates($QonLr,$coord,5,70,'Q = ')[red]; $DxQ Calculate( 5, 90,'d(x,Q) = ','#A1 #B1 - 2^ #A2 #B2 - 2^ + 0.5^')($Kx,$KQ)[black]; $SBT ShowButton( 2,350,'Trace')($Pprojx,$Clear)[blue,bold]; $HBT HideButton(50,350,'Stop')($Pprojx)[black]; $SBClear ShowButton( 2,370,'Clear')($Clear)[black]; $HBClear HideButton(50,370,'Clear')($Clear)[black]; $SimB SimultaneousButton( 2,390,'Trace')($SBT,$SBClear)[blue,bold];

This page requires a Java capable browser. Distance($x,$QonLr,5,90,'d(x,Q) = ')[red]; $IntxPPctr Intersect($Xax,$Lrefl)[white,label('Pctrx')]; Coordinates($IntxPPctr,$coord,10,10,'Pctrx = ')[red]; $IntyPPctr Intersect($Yax,$Lrefl)[white,label('Pctry')]; Coordinates($IntyPPctr,$coord,10,30,'Pctry = ')[red]; $CP Coordinates($P,$coord,20,60,'P = ')[red,hidden]; $CPctr Coordinates($O,$coord,20,100,'O = ')[red,hidden]; $P2_Pctr2 Calculate( 0,30,'','#B2 #A2 -')($CPctr,$CP)[red,suffix('x'),hidden]; $P1_Pctr1 Calculate(57,30,'+(','#A1 #B1 -')($CPctr,$CP)[red,suffix(')y = '),hidden]; $right1 Calculate(152,30,'','#B2#A2- #A1* #B1#A1- #A2* -')($CPctr,$CP)[red,hidden]; $Q2_Pctr2 Calculate( 0,50,'','#B2 #A2 -')($CPctr,$CQ)[blue,suffix('x'),hidden]; $Q1_Pctr1 Calculate(57,50,'+(','#A1 #B1 -')($CPctr,$CQ)[blue,suffix(')y = '),hidden]; $right2 Calculate(152,50,'','#B2#A2- #A1* #B1#A1- #A2* -')($CPctr,$CQ)[blue,hidden];