This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Huu hapa utatuzi wa swali lako: a) Step 1: Andika nukta zilizopewa. Nukta za pembe nne ni: A(-4, 3) B(-2, 3) C(-2, 1) D(-4, 1) Step 2: Jinsi ya kuchora nukta kwenye mchoro wa Cartesia. Ili kuchora nukta hizi, chora mhimili wa x (mlalo) na mhimili wa y (wima) unaokatana kwenye asili (0,0). Kisha, kwa kila nukta (x, y): • Anza kwenye asili. • Sogea x vitengo kushoto (kama x ni hasi) au kulia (kama x ni chanya). • Kutoka hapo, sogea y vitengo chini (kama y ni hasi) au juu (kama y ni chanya). • Weka alama kwenye eneo hilo. Baada ya kuchora nukta zote nne, ziunganishe kwa mpangilio (A hadi B, B hadi C, C hadi D, na D hadi A) ili kuunda pembe nne. Step 3: Kokotoa urefu wa kila upande. Tutatumia fomula ya umbali d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2). Urefu wa AB: AB = sqrt((-2 - (-4))^2 + (3 - 3)^2) AB = sqrt((2)^2 + (0)^2) AB = sqrt(4 + 0) AB = sqrt(4) = 2 vitengo Urefu wa BC: BC = sqrt((-2 - (-2))^2 + (1 - 3)^2) BC = sqrt((0)^2 + (-2)^2) BC = sqrt(0 + 4) BC = sqrt(4) = 2 vitengo Urefu wa CD: CD = sqrt((-4 - (-2))^2 + (1 - 1)^2) CD = sqrt((-2)^2 + (0)^2) CD = sqrt(4 + 0) CD = sqrt(4) = 2 vitengo Urefu wa DA: DA = sqrt((-4 - (-4))^2 + (3 - 1)^2) DA = sqrt((0)^2 + (2)^2) DA = sqrt(0 + 4) DA = sqrt(4) = 2 vitengo Step 4: Kokotoa miteremko ya kila upande. Tutatumia fomula ya mteremko m = (y_2 - y_1)/(x_2 - x_1). Mteremko wa AB: m_AB = (3 - 3)/(-2 - (-4)) = (0)/(2) = 0 (Mstari mlalo) Mteremko wa BC: m_BC = (1 - 3)/(-2 - (-2)) = (-2)/(0) (Mteremko haujafafanuliwa, mstari wima) Mteremko wa CD: m_CD = (1 - 1)/(-4 - (-2)) = (0)/(-2) = 0 (Mstari mlalo) Mteremko wa DA: m_DA = (3 - 1)/(-4 - (-4)) = (2)/(0) (Mteremko haujafafanuliwa, mstari wima) Step 5: Tambua umbo la umbo lililoundwa. • Tumegundua kuwa pande zote nne (AB, BC, CD, DA) zina urefu sawa wa vitengo 2. • Mstari AB na CD ni milalo (mteremko 0), hivyo ni sambamba. • Mstari BC na DA ni wima (mteremko haujafafanuliwa), hivyo ni sambamba. • Pande zinazopakana (kama AB na BC) ni perpendicular kwa sababu moja ni mlalo na nyingine ni wima. Kwa kuwa pande zote zina urefu sawa na pembe zote ni pembe mraba (digrii 90), umbo lililoundwa ni mraba. Umbo la umbo lililoundwa ni: Mraba Tuma swali linalofuata 📸