Question

Point C ( 2 , 3 ) divides the line segment joining A(3,5) and B internally in the ratio 1 : 2. The coordinates of B are ... *
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Answer 1

Step-by-step explanation:

pls mark as brainlist answer

Answer 2

Answer:

The coordinates of point B are ( 0, - 1 ).

Step-by-step-explanation:

We have given that point C divides the line segment AB in the ratio 1 : 2.

We have to find the coordinates of the point B.

$\bullet\sf\:A\:\equiv\:(\:3\:,\:5\:)\:\equiv\:(\:x_{1}\:,\:y_{1}\:)\\\\\bullet\sf\:B\:\equiv\:(\:x_{2}\:,\:y_{2}\:)\\\\\bullet\sf\:C\:\equiv\:(\:2\:,\:3\:)\:\equiv\:(\:x\:,\:y\:)$

Now, we know that,

$\pink{\sf\:x\:=\:\dfrac{\:mx_{2}\:+\:nx_{1}}{m\:+\:n}\:\:,\:\:y\:=\:\dfrac{my_{2}\:+\:ny_{1}}{m\:+\:n}}\:\sf\:\:-\:-\:[\:Section\:formula\:]\\\\:\implies\sf\:2\:=\:\dfrac{1\:(\:x_{2}\:)\:+\:2\:(\:3\:)}{1\:+\:2\:}\:\:,\:\:3\:=\:\dfrac{1\:(\:y_{2}\:)\:+\:2\:(\:5\:)}{1\:+\:2\:}\\\\:\implies\sf\:2\:=\:\dfrac{x_{2}\:+\:6}{3}\:\:,\:\:3\:=\:\dfrac{y_{2}\:+\:10}{3}\\\\:\implies\sf\:2\:\times\:3\:=\:x_{2}\:+\:6\:\:,\:\:3\:\times\:3\:=\:y_{2}\:+\:10\\\\:\implies\sf\:6\:=\:x_{2}\:+\:6\:\:,\:\:9\:=\:y_{2}\:+\:10\\\\:\implies\sf\:x_{2}\:=\:6\:-\:6\:\:,\:\:y_{2}\:=\:9\:-\:10\\\\:\implies\boxed{\red{\sf\:x_{2}\:=\:0\:\:,\:\:y_{2}\:=\:-\:1}}$

Additional Information:

1. Distance Formula:

The formula which is used to find the distance between two points using their coordinates is called distance formula.

$\large{\boxed{\red{\sf\:d\:(\:A\:,\:B\:)\:=\:\sqrt{\:(\:x_{1}\:-\:x_{2}\:)^{2}\:+\:(\:y_{1}\:-\:y_{2}\:)^{2}\:}}}\:\:}$

2. Section Formula:

The formula which is used to find the coordinates of a point which divides a line segment in a particular ratio is called section formula.

$\large{\boxed{\red{\sf\:x\:=\:\dfrac{mx_{2}\:+\:nx_{1}\:}{m\:+\:n}}}}\:\:\sf\:\&\:\:\:\large{\boxed{\red{\sf\:y\:=\:\dfrac{my_{2}\:+\:ny_{1}\:}{m\:+\:n}}}}$