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c) 2y - x and y - 2x + 3

Mathematics

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Answer

Mistari ni wima\text{Mistari ni wima}

Step-by-step solution

4 steps

Ili kubaini kama jozi za mistari ni wima (perpendicular), tunahitaji kulinganisha miteremko yao. Mistari miwili ni wima ikiwa bidhaa ya miteremko yao ni −1-1.

c) 2y−x2y - x na y=−2x+3y = -2x + 3

Kutokana na picha, nitaelewa equation ya kwanza kama 2y−x=02y - x = 0.

  1. Pata mteremko wa mstari wa kwanza.

    Badilisha 2y−x=02y - x = 0 kuwa umbo la y=mx+cy = mx + c.

    2y=x2y = x y=12xy = \frac{1}{2}x

    Mteremko wa mstari wa kwanza ni m1=12m_1 = \frac{1}{2}.

  2. Pata mteremko wa mstari wa pili.

    Mstari wa pili tayari uko katika umbo la y=mx+cy = mx + c.

    y=−2x+3y = -2x + 3

    Mteremko wa mstari wa pili ni m2=−2m_2 = -2.

  3. Zidisha miteremko.

    m1⋅m2=12⋅(−2)=−1m_1 \cdot m_2 = \frac{1}{2} \cdot (-2) = -1
  4. Hitimisho.

    Kwa kuwa bidhaa ya miteremko ni −1-1, mistari hii ni wima.
    Mistari ni wima\text{Mistari ni wima}

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