The point that partitions segment AB in a 2: 1 ratio is point (5,19/3).
Suppose the point that partitions segment AB in a 2: 1 ratio is point (x,y)
What is the internal division formula?
The internal division formula for a line segment is given by:
[tex]x=\frac{m_1x_2+m_2x_1}{m_1+m_2}[/tex]
[tex]y=\frac{m_1y_2+m_2y_1}{m_1+m_2}[/tex]
Where (x₁,y₁) and (x₂,y₂) are endpoints of the line segment.
Coordinates of points A≡(1,3)
Coordinates of points B≡(7,8)
[tex]x=\frac{2*7+1*1}{1+2}[/tex]
[tex]x=5[/tex]
Similarly, [tex]y=\frac{19}{3}[/tex]
So (x,y)≡(5,19/3)
Hence, the point that partitions segment AB in a 2: 1 ratio is point (5,19/3).
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