Mibvunzo Yemuenzaniso Kukurukura Tsananguro yeDenderedzwa
Denderedzwa ndeimwe yemaumbirwo ejometri atinosangana nawo kakawanda muhupenyu hwezuva nezuva. Mumasvomhu, madenderedzwa ane tsananguro dzakasiyana uye hunhu. Chinyorwa chino chichaongorora tsananguro yedenderedzwa nezvinhu zvaro zvine chekuita naro zvakadzama, pamwe nekupa mienzaniso yakawanda yezvinetso uye mhinduro dzazvo kuti tinzwisise madenderedzwa.
Tsanangudzo yeDenderedzwa
Denderedzwa iboka remapoinzi ese ari mudenderedzwa ari kure nepakati pedenderedzwa. Daro riri pakati pepakati nechero poindi iri mudenderedzwa rinonzi radius yedenderedzwa. Equation yedenderedzwa rine pakati panzvimbo \((h, k)\) uye radius \(r\) inopiwa na:
\[ (x – h)^2 + (y – k)^2 = r^2 \]
Ikoko:
– \((h, k)\) ndiwo makoronesheni ari pakati pedenderedzwa,
– \(r\) ndiyo nharaunda yedenderedzwa,
– \(x\) uye \(y\) ndiwo makoronesheni enzvimbo ipi neipi iri mudenderedzwa.
Zvinhu zveDenderedzwa
Tisati tapinda mumibvunzo yemuenzaniso, zvakanaka kuziva zvimwe zvezvinhu zvakakosha zviri mudenderedzwa:
1. Pakati peDenderedzwa: Nzvimbo yakamira iri pakati penzvimbo dzese dziri kure nedaro rakafanana.
2. Radius (r): Chinhambwe kubva pakati pedenderedzwa kusvika chero panzvimbo iri padenderedzwa.
3. Dhayamita (d): Mutsetse wakatwasuka unopfuura nepakati pedenderedzwa wobatanidza mapoinzi maviri padenderedzwa, une hurefu hwakapetwa kaviri kupfuura radius (\(d = 2r\)).
4. Arc: Chikamu chedenderedzwa redenderedzwa chiri pakati penzvimbo mbiri dziri padenderedzwa.
5. Chord: Mutsetse wakatwasuka unobatanidza mapoinzi maviri padenderedzwa asi usingapfuuri nepakati.
6. Apothem: Chinhambwe chipfupi kubva pakati pedenderedzwa kusvika pachord.
7. Angle Yepakati: Angle inoumbwa nema radii maviri kubva pakati pedenderedzwa.
8. Perimeter Angle: Kona inoumbwa nemachords maviri anobatana panzvimbo imwe chete padenderedzwa.
Mibvunzo yemuenzaniso nehurukuro
Muenzaniso Mubvunzo 1
Mubvunzo: Kupiwa denderedzwa rine pakati panzvimbo \((3, 4)\) uye richipfuura nepakati \((7, 4)\). Sarudza equation yedenderedzwa.
Kukurukurirana:
Kuti tiwane equation yedenderedzwa, tinofanira kutanga taziva radius yaro. Sezvo denderedzwa richipfuura nepakati pepoindi \((7, 4)\), tinogona kuverenga daro riri pakati pepoindi iyi nepakati pedenderedzwa, rinova \((3, 4)\).
\[
r = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}
\]
\[
r = \sqrt{(7 - 3)^2 + (4 - 4)^2}
\]
\[
r = \sqrt{4^2 + 0^2}
\]
\[
r = 4
\]
Nepakati pa \((3, 4)\) uye radius 4, equation yedenderedzwa ndeiyi:
\[
(x – 3)^2 + (y – 4)^2 = 4^2
\]
\[
(x – 3)^2 + (y – 4)^2 = 16
\]
Muenzaniso Mubvunzo 2
Mubvunzo: Sarudza nzvimbo nedenderedzwa redenderedzwa rine dhayamita ye5 cm.
Kukurukurirana:
– Nzvimbo yedenderedzwa (A) inogona kuverengerwa uchishandisa fomura \(A = \pi r^2\),
\[
A = \pi \kawa 5^2
\]
\[
A = 25\pi \text{cm}^2
\]
Kana \(\pi \approx 3.14\), saka:
\[
A \inenge 25 \kawa 3.14 = 78.5 \text{cm}^2
\]
– Kutenderera kwedenderedzwa (C) kunogona kuverengerwa uchishandisa fomura \(C = 2\pi r\),
\[
C = 2 \nguva \pi \nguva 5
\]
\[
C = 10\pi \chinyorwa{cm}
\]
Kana \(\pi \approx 3.14\), saka:
\[
C \inenge gumi \kawa 3.14 = 31.4 \chinyorwa{cm}
\]
Muenzaniso Mubvunzo 3
Mubvunzo: Denderedzwa rine pakati penzvimbo O uye radius ye7 cm. Kana chord yehurefu hwe10 cm yakadhirowa padenderedzwa, sarudza daro pfupi kubva pakati peO kusvika pachord.
Kukurukurirana:
Kuti tiwane daro pfupi kubva pakati kuenda kuchord, tinoshandisa pfungwa yeapothem, inova daro pfupi kubva pakati kuenda kuchord. Ne radius ye 7 cm uye urefu hwechord ye 10 cm, tinogona kugadzirisa dambudziko iri tichishandisa triangle yekurudyi yakagadzirwa.
Kana pakati pechord iri poindi C, saka OC ndiyo poindi yatiri kutsvaga. Kana A naB vari iwo magumo echord, saka AC naBC zvese zviri 5 cm (hafu ye10 cm).
Kubva patriangle OAC iyo yakakomberedzwa kurudyi paC, tinoshandisa dzidziso yePythagorean:
\[
OA^2 = OC^2 + AC^2
\]
\[
7^2 = OC^2 + 5^2
\]
\[
49 = OC^2 + 25
\]
\[
OC^2 = 49 – 25
\]
\[
OC^2 = 24
\]
\[
OC = \sqrt{24} = 2\sqrt{6} \mashoko{cm}
\]
Muenzaniso Mubvunzo 4
Mubvunzo: Kupiwa denderedzwa rine equation \(x^2 + y^2 + 6x – 8y + 9 = 0\). Sarudza pakati nepakati pedenderedzwa.
Kukurukurirana:
Kuti tiwane pakati nepakati, tinoshandura equation kuita fomu yakajairika:
\[
x^2 + y^2 + 6x – 8y + 9 = 0
\]
Tinogadzirisa nekunatsiridza chimiro che quadratic:
\[
x^2 + 6x + y^2 – 8y = -9
\]
Kuwedzera nekubvisa (6/2)\(^2\) ku x-term uye (8/2)\(^2\) ku y-term:
\[
x^2 + 6x + 9 + y^2 – 8y + 16 = -9 + 9 + 16
\]
\[
(x + 3)^2 + (y – 4)^2 = 16
\]
Kubva muequation \((x + 3)^2 + (y – 4)^2 = 16\), tinoona kuti pakati pedenderedzwa ndi \((-3, 4)\) uye radius ndi \(r = \sqrt{16} = 4\).
Mhedziso
Denderedzwa ipfungwa huru uye yakakosha mu geometry. Kuburikidza nematambudziko emuenzaniso nehurukuro dziri pamusoro apa, tinogona kuwana kunzwisisa kwakadzama kwezvinhu zvakasiyana-siyana uye hunhu hwemadenderedzwa. Kuziva nyaya iyi kuchaita kuti zvive nyore kunzwisisa nekugadzirisa matambudziko akaomarara e geometry.
