Piv txwv ntawm Cov Lus Nug thiab Kev Sib Tham Txog Kev Txhais Lus Txog lej
Kev txhais lus yog kev hloov pauv geometric uas txav txhua qhov chaw ntawm lub dav hlau mus rau qhov deb tshwj xeeb hauv ib qho kev taw qhia tshwj xeeb. Hauv kev suav lej, kev txhais lus feem ntau yog siv los txav ib yam khoom mus rau hauv ib qho kev taw qhia yam tsis hloov nws cov duab lossis kev taw qhia. Hauv tsab xov xwm no, peb yuav tham txog ntau qhov piv txwv ntawm cov teeb meem thiab kev sib tham txog kev txhais lus lej kom pab cov nyeem ntawv nkag siab zoo dua txog lub tswv yim no.
Cov Ntsiab Lus Tseem Ceeb ntawm Kev Txhais Lus
Kev txhais lus hauv ob-seem kev sib koom ua ke tuaj yeem qhia tau los ntawm kev siv cov cim vector. Yog tias qhov taw tes A(x, y) raug txhais los ntawm vector \((a, b)\), ces qhov tshwm sim ntawm qhov taw tes A' (\(x'\), \(y'\)) tuaj yeem suav tau los ntawm kev siv cov mis:
\[ x' = x + a \]
\[ y' = y + b \]
Qhov twg:
- \( (x, y) \) yog qhov pib sib koom ua ke,
- \( (a, b) \) yog tus vector txhais lus,
- \( (x', y') \) yog cov kev sib koom ua ke ntawm cov txiaj ntsig txhais lus.
Cov Lus Nug Piv Txwv thiab Kev Sib Tham
Nov yog qee cov piv txwv ntawm cov lus nug txog kev txhais lus lej thiab lawv cov kev sib tham:
Piv txwv lus nug 1:
Lo lus nug:
Taw tes A nyob ntawm qhov sib koom ua ke (3, 4). Txhais taw tes A nrog lub vector \( (5, -2) \). Txheeb xyuas cov sib koom ua ke tshiab ntawm taw tes A.
Kev Sib Tham:
Nws paub tias:
\[ \text{Cov kev sib koom ua ke thawj ntawm qhov A} = (3, 4) \]
\[ \text{Kev txhais lus vector} = (5, -2) \]
Siv cov qauv txhais lus:
\[ x' = x + a \]
\[ y' = y + b \]
Hloov cov nqi:
\[ x' = 3 + 5 = 8 \]
\[ y' = 4 + (-2) = 2 \]
Yog li, cov kev sib koom ua ke tshiab ntawm qhov A tom qab txhais lus yog \( (8, 2) \).
Piv txwv lus nug 2:
Lo lus nug:
Ib daim duab peb ceg muaj cov vertex coordinates \( A(1, 2) \), \( B(3, 5) \), thiab \( C(6, 1) \). Txhais daim duab peb ceg nrog lub vector \( (-2, 4) \). Txheeb xyuas cov vertex coordinates ntawm daim duab peb ceg tom qab txhais lus.
Kev Sib Tham:
Cov kev sib koom ua ke ntawm lub vertex ntawm lub duab peb sab thiab cov vector txhais lus tau paub.
Cov coordinates ntawm point A':
\[ x' = 1 + (-2) = -1 \]
\[ y' = 2 + 4 = 6 \]
Ces, \( A' = (-1, 6) \).
Cov coordinates ntawm point B':
\[ x' = 3 + (-2) = 1 \]
\[ y' = 5 + 4 = 9 \]
Ces, \( B' = (1, 9) \).
Cov coordinates ntawm point C':
\[ x' = 6 + (-2) = 4 \]
\[ y' = 1 + 4 = 5 \]
Ces, \( C' = (4, 5) \).
Yog li, tom qab kev txhais lus, cov kev sib koom ua ke ntawm cov vertices ntawm daim duab peb sab tshiab yog \( A'(-1, 6) \), \( B'(1, 9) \), thiab \( C'(4, 5) \).
Piv txwv lus nug 3:
Lo lus nug:
Muab qhov chaw P ntawm qhov sib koom ua ke \( (-3, 0) \). Txheeb xyuas qhov tshwm sim ntawm kev txhais lus ntawm qhov chaw P los ntawm vector \( (7, -5) \).
Kev Sib Tham:
Muab cov coordinates ntawm P thiab cov vector txhais lus.
Siv cov qauv txhais lus:
\[ x' = x + a \]
\[ y' = y + b \]
Hloov cov nqi:
\[ x' = -3 + 7 = 4 \]
\[ y' = 0 + (-5) = -5 \]
Yog li, cov kev sib koom ua ke ntawm cov txiaj ntsig txhais lus ntawm qhov P yog \((4, -5) \).
Piv txwv lus nug 4:
Lo lus nug:
Point Q nyob ntawm qhov sib koom ua ke \( (4, -3) \). Yog tias point Q raug txhais kom cov sib koom ua ke tshiab dhau los ua \( (9, 1) \), txiav txim siab qhov vector txhais lus siv.
Kev Sib Tham:
Nws paub tias:
\[ \text{Cov kev sib koom ua ke pib} = (4, -3) \]
\[ \text{Cov kev sib koom tes ntawm cov txiaj ntsig} = (9, 1) \]
Siv cov qauv txhais lus los nrhiav cov vector \( (a, b) \):
\[ x' = x + a \]
\[ y' = y + b \]
Cov txiaj ntsig txhais lus tau paub lawm:
\[ 9 = 4 + ib \]
\[ 1 = -3 + b \]
Yog li, tus vector txhais lus tuaj yeem suav raws li hauv qab no:
\[ ib = 9 – 4 = 5 \]
\[ b = 1 + 3 = 4 \]
Yog li, tus vector txhais lus siv yog \( (5, 4) \).
Piv txwv lus nug 5:
Lo lus nug:
Cov duab plaub fab ABCD muaj cov ces kaum \( A(1, 2) \), \( B(1, 5) \), \( C(4, 5) \), thiab \( D(4, 2) \). Txhais cov duab plaub fab nrog lub vector \( (3, -1) \). Txheeb xyuas cov kev sib koom tes tshiab ntawm cov duab plaub fab ABCD.
Kev Sib Tham:
Nws paub tias:
\[ \text{Kev txhais lus vector} = (3, -1) \]
Cov coordinates ntawm point A':
\[ x' = 1 + 3 = 4 \]
\[ y' = 2 + (-1) = 1 \]
Ces, \( A' = (4, 1) \).
Cov coordinates ntawm point B':
\[ x' = 1 + 3 = 4 \]
\[ y' = 5 + (-1) = 4 \]
Ces, \( B' = (4, 4) \).
Cov coordinates ntawm point C':
\[ x' = 4 + 3 = 7 \]
\[ y' = 5 + (-1) = 4 \]
Ces, \( C' = (7, 4) \).
Cov coordinates ntawm point D':
\[ x' = 4 + 3 = 7 \]
\[ y' = 2 + (-1) = 1 \]
Ces, \( D' = (7, 1) \).
Yog li, cov kev sib koom ua ke tshiab ntawm quadrilateral ABCD tom qab txhais lus yog \(A'(4, 1) \), \(B'(4, 4) \), \(C'(7, 4) \), thiab \(D'(7, 1) \).
Xaus
Kev txhais lus yog ib qho kev hloov pauv yooj yim heev tab sis tseem ceeb hauv geometry. Kev paub txog cov txheej txheem no tso cai rau peb ua ntau yam haujlwm geometric, xws li kev hloov cov khoom yam tsis hloov lawv cov duab lossis qhov loj.
Los ntawm kev nkag siab txog lub tswv yim ntawm kev txhais lus los ntawm ntau yam teeb meem piv txwv uas tau tham saum toj no, vam tias cov nyeem ntawv yuav nkag siab zoo dua thiab siv lub tswv yim no rau ntau yam teeb meem thiab hauv lub neej tiag tiag. Kev txhais lus tsis yog tsuas yog muaj txiaj ntsig zoo hauv kev lej xwb tab sis kuj muaj txiaj ntsig zoo rau ntau yam kev kawm, suav nrog physics, computer graphics, thiab kev tsim qauv.
