in what ratio is the line segment joining the point (2, – 4 )and( 3,8) form of a divided by the x axis also find the point of division​

Question

in what ratio is the line segment joining the point (2, – 4 )and( 3,8) form of a divided by the x axis also find the point of division​

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Eva 2 months 2021-11-23T06:32:58+00:00 1 Answer 0 views 0

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    2021-11-23T06:34:28+00:00

    Answer

    The ratio is 1:2

    and the point of division is (7/3 , 0)

    \bf\large\underline{Given}

    • The points are (2 , -4) and (3 , 8)

    \bf\large\underline{To \: Find}

    • The ratio in which X-axis divides the line
    • The point of division

    \bf\large\underline{Solution}

    Let the point of dividend by X-axis of the line joining the points be (x , 0) and the ratio be m:n

    Also let the points be A(2 , -4) and B(3 , 8)

    \sf \underline{Applying \ section\ formula :}

    \sf\implies x = \dfrac{3m + 2n}{m+n} \longrightarrow (1)

    And

    \sf\implies 0 = \dfrac{8m - 4n}{m + n} \\\\ \sf\implies 8m - 4n = 0 \\\\ \sf\implies 8m = 4n \\\\ \sf\implies 2m = n \\\\ \sf\implies \dfrac{m}{n} = \dfrac{1}{2} \\\\ \sf\implies m:n = 1:2

    Putting the value of m and n in (1) we have :

    \sf\implies x = \dfrac{3\times 1 + 2\times 2}{1+2}\\\\ \sf\implies x = \dfrac{7}{3}

    Therefore , the point of division is 7/3

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