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7.2: Mistari Sambamba

  • Page ID
    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.

    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.

    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\((0, −3)\).