<prompt> Tafuta uhakika kwenye mstariy fracx 52ambayo iko karibu zaidi na uhakika 6,1.  <response>: Kumbuka kuwa 1,3 na 3,4 ni alama mbili kwenye mstari, kwa hivyo mstari una vekta ya mwelekeo waanzapmatrix 3 4 mwishopmatrix - anzapmatrix 1 3 mwishopmatrix anzapmatrix 2 1 mwishopmatrix. asyukubwa wa kitengo 0.5 cm;jozi A, B, C, D, V, P;A -8, -8 52;B 5, 5 52;C 1,3;D 3,4;V 6,1;P V tafakariA,BV2;chora-8,0--8,0;chora0,-4--0,5;choraA--B,nyekundu;kuchoraV--P,dashed;choraC--V,Arrow6;choraC--D,Arrow6;nukta6,1, V, E;nukta1,3, C, NW;nukta3,4, D, NW;asyVekta inayotoka 1,3 hadi 6,1 ni beginpmatrix 6 1 endpmatrix - beginpmatrix 1 3 endpmatrix anzapmatrix 5 -2 mwishopmatrix. Kukadiria vekta hii kwenye vekta ya mwelekeo, tunapatajina la operetaproj_anzapmatrix 2 1 mwishopmatrix anzapmatrix 5 -2 mwishopmatrix fracanzapmatrix 5 -2 mwishopmatrix cdot anzapmatrix 2 1 mwishopmmatrixleft anzapmatrix 2 1 mwishopmatrix kulia2 anzapmatrix 2 1 mwishopmatrix frac85 anzapmatrix 2 1 endpmatrix anzapmatrix frac165 frac85 endpmatrix.asyusepackageamsmath;ukubwa wa kitengo 0.5 cm;jozi A, B, C, D, V, P;A -8, -8 52;B 5, 5 52;C 1,3;D 3,4;V 6,1;P V tafakariA,BV2;chora-8,0--8,0;chora0,-4--0,5;choraA--B,nyekundu;kuchoraV--P,dashed;choraC--V,Arrow6;choraC--P,Arrow6;lebobeginpmatrix frac165 frac85 endpmatrix, P, NW;nukta6,1, V, E;nukta1,3, C, NW;asyKishaanzapmatrix 1 3 mwishopmatrix anzapmatrix frac165 frac85 endpmatrix anzapmatrix frac215 frac235 endpmatrix,kwa hivyo uhakika kwenye mstari ulio karibu zaidi na 6,1 ni left frac 215, frac235 kulia. 