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7.2: Mistari Sambamba

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    164596

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    Ufafanuzi: Lines Sambamba

    Katika ndege ya kuratibu, mistari sambamba ni mistari ambayo haipatikani au kuingiliana. Wao daima ni umbali sawa mbali. Aidha, mistari sambamba ina mteremko huo.

    Mfano Template:index

    Pata mteremko wa mstari\(l\) unaopita\((2, 0)\)\((4, −3)\) na mteremko wa mstari\(q\) unaopita\((2, −3)\) na\((4, −6)\). Kuamua kama mistari ni sambamba.

    Suluhisho

    Tumia mteremko wa fomu ya mstari ili kupata mteremko wa mstari\(l\)\(m_l\),, na mteremko wa mstari\(q\)\(m_q\), kama ifuatavyo,

    \(\begin{array} &&m_l = \dfrac{y_2 − y_1}{x_2 − x_1}\;\;\;\;\;\;\;\;\;\; &m_q = \dfrac{y_2 − y_1}{x_2 − x_1} \\ &= \dfrac{−3 − 0}{4 − 2}\;\;\;\;\;\;\;\;\;\; &= \dfrac{−6 − (−3)}{4 − 2} \\ &= \dfrac{−3}{2}\;\;\;\;\;\;\;\;\;\; &= \dfrac{−3}{2} \end{array}\)

    Kwa kuwa mteremko miwili ni sawa, basi, mistari\(l\) na\(q\) ni sawa.

    Zoezi Template:index

    Kuamua kama mistari iliyotolewa ni sawa:

    1. Mstari\(l\) unaopita kupitia pointi\((2, 2)\)\((3, 3)\) na na mstari\(q\) unaopita kupitia pointi\((4, 1)\) na\((0, 5)\).
    2. Mstari\(l\) unaopita kupitia pointi\((1, 3)\)\((6, −2)\) na na mstari\(q\) unaopita kupitia pointi\((−2, −7)\) na\((10, 5)\).
    3. Mstari\(l\) unaopita kupitia pointi\((−6, 5)\)\((2, −1)\) na na mstari\(q\) unaopita kupitia pointi\((−4, 0)\) na\((0, −3)\).