given that oa=2x+9y ob=4x+8y and cd= 4x-2y, explain the geometrical relationships between the straight lines ab and cd mathswatch answer

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given that oa=2x+9y ob=4x+8y and cd= 4x-2y, explain the geometrical relationships between the straight lines ab and cd mathswatch answer

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Savannah 2 weeks 2021-10-13T23:29:00+00:00 1 Answer 0

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    2021-10-13T23:30:23+00:00

    The geometrical relationships between the straight lines ab and cd

    is the straight line ab is parallel to the straight line cd

    Step-by-step explanation:

    Let us revise some notes:

    • If a line is drawn from the origin and passes through point A (a , b), then the equation of OA = ax + by
    • If a line is drawn from the origin and passes through point B (c , d), then the equation of OB = cx + dy
    • To find the equation of AB subtract OB from OA, then AB = (c – a)x + (d – b)y
    • The slope of line AB = \frac{-coefficient(x)}{coefficient(y)}

    ∵ oa = 2 x + 9 y

    ∵ ob = 4 x + 8 y

    ∵ ab = OB – OA

    ∴ ab = (4 x + 8 y) – (2 x + 9 y)

    ∴ ab = 4 x + 8 y – 2 x – 9 y

    – Add like terms

    ∴ ab = (4 x – 2 x) + (8 y – 9 y)

    ∴ ab = 2 x + -y

    ∴ ab = 2 x – y

    ∵ The slope of ab = \frac{-coefficient(x)}{coefficient(y)}

    ∵ Coefficient of x = 2

    ∵ Coefficient of y = -1

    ∴ The slope of ab = \frac{-2}{-1}=2

    ∵ cd = 4 x – 2 y

    ∵ Coefficient of x = 4

    ∵ Coefficient of y = -2

    ∴ The slope of cd = \frac{-4}{-2}=2

    ∵ Parallel lines have same slopes

    ∵ Slope of ab = slope of cd

    ∴ ab // cd

    The geometrical relationships between the straight lines ab and cd

    is the straight line ab is parallel to the straight line cd

    Learn more;

    You can learn more about the parallel lines in brainly.com/question/10483199

    #LearnwithBrainly

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