Mienzaniso yeMibvunzo Inokurukura Nzvimbo yePoindi Kana Uchienderana neDenderedzwa
Kuziva nzvimbo yepoindi kana denderedzwa inyaya inokosha mu geometry yekutanga, kunyanya mukudzidza madenderedzwa. Muchinyorwa chino, tichakurukura mienzaniso yakati wandei yematambudziko ane chekuita nenzvimbo yepoindi kana denderedzwa, pamwe chete netsananguro dzawo. Izvi zvichabatsira kujekesa pfungwa iyi kuburikidza nemashandisirwo anoshanda.
Pendauluan
Tisati tapinda mumibvunzo yemuenzaniso, ngatiyeukei nzvimbo nhatu dzinogona kunge dziripo dzepoindi padenderedzwa:
1. Mukati medenderedzwa: Kana daro renzvimbo kusvika pakati pedenderedzwa riri diki pane dhayamita yedenderedzwa.
2. Kunze kwedenderedzwa: Kana daro renzvimbo kusvika pakati pedenderedzwa rakakura kupfuura dhayamita yedenderedzwa.
3. Padenderedzwa: Kana daro kubva panzvimbo kusvika pakati pedenderedzwa rakafanana neredhiyo yedenderedzwa.
Pamasvomhu, nzvimbo yepoindi \(T(x_1, y_1)\) maererano nedenderedzwa rakanangana pa \((a, b)\) neradius \(r\) inogona kuwanikwa nekuenzanisa \(T(x_1, y_1)\) ne equation yedenderedzwa, kureva:
\[
(x – a)^2 + (y – b)^2 = r^2
\]
Kana mhedzisiro yekutsiva \(x_1\) uye \(y_1\) mu equation ichipa kukosha:
– Diki pane \(r^2\), poindi iri mukati medenderedzwa.
– Kupfuura \(r^2\), poindi yacho iri kunze kwedenderedzwa.
– Zvakafanana ne \(r^2\), pfungwa iri padenderedzwa.
Mibvunzo yemuenzaniso nekukurukurirana
Mubvunzo 1
Sarudza nzvimbo yepoindi \(T(3, 4)\) maererano nedenderedzwa rine equation \( (x – 1)^2 + (y – 2)^2 = 25 \).
Kukurukurirana:
Danho rekutanga nderekuongorora equation yedenderedzwa uye kuwana daro kubva pane poindi \(T(3, 4)\) kusvika pakati pedenderedzwa \((1, 2)\).
1. Ziva pakati nepakati pedenderedzwa:
Equation yedenderedzwa: \( (x – 1)^2 + (y – 2)^2 = 25 \)
– Pakati pedenderedzwa (\(a, b\)): (1, 2)
– Nharaunda yedenderedzwa (\(r\)): \(\sqrt{25} = 5\)
2. Verenga daro riri pakati pepoindi \(T(3, 4)\) nepakati pedenderedzwa \((1, 2)\):
\[
D = \sqrt{(3 – 1)^2 + (4 – 2)^2} = \sqrt{2^2 + 2^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2}
\]
Kukosha \( 2\sqrt{2} \approx 2 \times 1.414 = 2.828 \) (zvishoma pane \(5\)).
3. Mhedziso:
Sezvo \( 2\sqrt{2} < 5 \), ipapo poindi \( T(3, 4) \) iri mukati medenderedzwa. Mubvunzo 2 Denderedzwa rine pakati panzvimbo \( (0, 0) \) uye radius ye7. Sarudza nzvimbo yepoindi \(P(5, 6)\) maererano nedenderedzwa.
Mubvunzo 3
Sarudza nzvimbo yepoindi \(M(2, -1)\) maererano nedenderedzwa rine equation \( x^2 + y^2 = 5 \).
Kukurukurirana:
1. Verenga daro kubva panzvimbo \(M(2, -1)\) kusvika pakati pedenderedzwa \( (0, 0):
\[
D = \sqrt{(2 – 0)^2 + (-1 – 0)^2} = \sqrt{4 + 1} = \sqrt{5}
\]
2. Enzanisa daro \(D\) neredhiyo yedenderedzwa:
Nharaunda yedenderedzwa (\(r\)) = \(\sqrt{5}\).
3. Mhedziso:
Sezvo \( \sqrt{5} = \sqrt{5} \), ipapo poindi \( M(2, -1) \) iri padenderedzwa.
Mubvunzo 4
Denderedzwa rine pakati pa \( (4, 3) \) rine radius \(\sqrt{10}\). Ratidza nzvimbo yepoindi \( N(7, 7) \) maererano nedenderedzwa iri.
Kukurukurirana:
1. Denderedzwa reEquation:
Equation yedenderedzwa rine pakati \( (4, 3) \) uye radius \( \sqrt{10} \) ndeiyi:
\[
(x – 4)^2 + (y – 3)^2 = 10
\]
2. Verenga daro kubva panzvimbo \( N(7, 7) \) kusvika pakati pedenderedzwa \( (4, 3) \):
\[
D = \sqrt{(7 – 4)^2 + (7 – 3)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5
\]
3. Mhedziso:
Sezvo \( 5 > \sqrt{10} \), ipapo poindi \( N(7, 7) \) iri kunze kwedenderedzwa.
Penutup
Nekunzwisisa maverengero enzvimbo kubva pakati pedenderedzwa uye kuenzanisa neradius, tinogona kuona zviri nyore nzvimbo yenzvimbo kana tichienzanisa nedenderedzwa. Kukurukurirana kuri muchinyorwa chino kunotarisirwa kupa kunzwisisa kwakajeka kwepfungwa iyi uye magadzirisiro ematambudziko ane chekuita nenzvimbo yenzvimbo kana tichienzanisa nedenderedzwa.
Mukuita, kuziva nzvimbo yepfungwa idzi kunobatsira zvikuru mukushandiswa kwakasiyana-siyana kwemasvomhu, kusanganisira kuongorora geometric, dhizaini yemifananidzo, uye mainjiniya. Saka, kugona pfungwa iyi inheyo yakakosha inofanirwa kutariswa nekunzwisiswa kwakadzama.
