The point Q divides segment joining A (3, 5) and B (7, 9) in the ratio 2 : 3. Find the X-coordinate of Q.

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1. [tex]\textbf{Given:}[/tex]

   [tex]\textsf{The point Q divides line segment joining A(3,5) and}[/tex]

   [tex]\textsf{B(7,9) in the ratio 2:3}[/tex]

   [tex]\textbf{To find:}[/tex]

   [tex]\textsf{The co-ordinates of Q}[/tex]

   [tex]\textbf{Solution:}[/tex]

   [tex]\textsf{By Section formula, the co-ordinates of Q are}[/tex]

   [tex]\mathsf{\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)}[/tex]

   [tex]\mathsf{\left(\dfrac{2(7)+3(3)}{2+3},\dfrac{2(9)+3(5)}{2+3}\right)}[/tex]

   [tex]\mathsf{\left(\dfrac{14+9}{5},\dfrac{18+15}{5}\right)}[/tex]

   [tex]\mathsf{\left(\dfrac{23}{5},\dfrac{33}{5}\right)}[/tex]

   [tex]\therefore\mathsf{x\;co-ordinate\;of\;Q\;is\;\dfrac{23}{5}}[/tex]

   [tex]\textbf{Find more:}[/tex]

   Find the ratio in which the line segment joining the points (-3,10), and(6,-8) is divided by(-1,6)​

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