Math, asked by Rectangle1234, 2 months ago

Solve the attachment!!!

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Answers

Answered by ᏞiteralFairy
12

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Reffer to the attachment!!

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Answered by MrImpeccable
37

ANSWER:

Given:

  • Two points A(5,-6) and B(-1,-4)
  • y-axis divides the line segment AB.

To Find:

  • Ratio in which AB is divided
  • Point of intersection

Solution:

\text{\sf{Let the point dividing AB be C, with coordinates (x,y)}}\\\\\text{\sf{But, it is given that y-axis divides AB. So, coordinates of C = (0,y)}}\\\\\text{\sf{Section Formula}}:\longrightarrow\sf{(x,y) = \left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)} \\\\\text{\sf{Where, $x_1,x_2, y_1, y_2$ are coordinates of the two points and,}}\\\text{\sf{m:n is the ratio in which the line is divided.}}\\\\\text{\sf{Here,$x_1=5,x_2=-1,y_1=-6,y_2=-4$ and x = 0. So,}}

:\implies\sf{(0,y) = \left(\dfrac{m(-1)+n(5)}{m+n},\dfrac{m(-4)+n(-6)}{m+n}\right)}\\\\:\implies\sf{(0,y) = \left(\dfrac{-m+5n}{m+n},\dfrac{-4m-6n}{m+n}\right)}\\\\\text{\sf{Taking x coordinates,}}\\\\:\implies\sf{0 = \dfrac{-m+5n}{m+n}}\\\\:\implies\sf{5n-m=0}\\\\:\implies \sf{m=5n}\\\\\bf{:\implies \dfrac{m}{n}=5\implies m:n = 5:1}\\\\\text{\sf{Hence,}} \\\\:\implies\sf{y=\dfrac{-4(5)+-6(1)}{5+1}}\\\\:\implies\sf{y=\dfrac{-20-6}{6} \implies \dfrac{-26}{6}=\dfrac{-13}{3}}

\text{\sf{Hence, the point of intersection C(0,y) is}} \\\\\bf{:\implies C = (0,y) = \left(0,\dfrac{-13}{3}\right)}

\text{\bf{FINAL ANSWER:}}\\\\\bf{Ratio=5:1\:\:\:\&\:\:\:C=\left(0,\dfrac{-13}{3}\right)}

Formula Used:

\:\:\:\:\:\:\bullet\:\:\:\text{\sf{Section Formula}}:\longrightarrow\sf{(x,y) = \left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}

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