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Divisor of a Line Segment

7.1 Divisor of a Line Segment
 
A visual representation of a divisor of a line segment defined in a mind map.
 
Ratio Division
Figure

A graph featuring two lines, one of which ascends, representing the division of a line segment between two points in a ratio.
Description
  • The point \(P(x,y)\) divides the line segment joining two points \(A(x_1,y_1)\) and \(B(x_2,y_2)\) in the ratio \(m:n\).
  • The coordinates of point \(P(x,y)\) are given by:

\(P\left(\dfrac{nx_1+mx_2}{m+n},\dfrac{ny_1+my_2}{m+n} \right)\)
 
Midpoint (Ratio \(1:1\))
Figure

A graph displaying two lines, with one line ascending, and a midpoint M dividing the segment between points A and B equally.
Description
  • The midpoint \(M(x,y)\) of the line segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\) is: 

\(M\left( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2} \right)\)
 
Example Problems
Finding a Dividing Point
  • Given points \(A(2,3)\) and \(B(8,7)\), find the point \(P\) that divides \(AB\) in the ratio \(2:3\).
  • Solution:

\(\begin{aligned} x&=\dfrac{2\times8+3\times2}{2+3}=\dfrac{16+6}{5}=4.4, \\ \\ y&=\dfrac{2\times7+3\times3}{2+3}=\dfrac{14+9}{5}=4.6. \end{aligned}\)

  • Point \(P\) is \((4.4,4.6)\).
Midpoint Calculation
  • Find the midpoint of the line segment joining \((1,2)\) and \((5,6)\).
  • Solution:

\(M\left( \dfrac{1+5}{2},\dfrac{2+6}{2} \right)=(3,4)\).
 
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of pandai.

Divisor of a Line Segment

7.1 Divisor of a Line Segment
 
A visual representation of a divisor of a line segment defined in a mind map.
 
Ratio Division
Figure

A graph featuring two lines, one of which ascends, representing the division of a line segment between two points in a ratio.
Description
  • The point \(P(x,y)\) divides the line segment joining two points \(A(x_1,y_1)\) and \(B(x_2,y_2)\) in the ratio \(m:n\).
  • The coordinates of point \(P(x,y)\) are given by:

\(P\left(\dfrac{nx_1+mx_2}{m+n},\dfrac{ny_1+my_2}{m+n} \right)\)
 
Midpoint (Ratio \(1:1\))
Figure

A graph displaying two lines, with one line ascending, and a midpoint M dividing the segment between points A and B equally.
Description
  • The midpoint \(M(x,y)\) of the line segment joining \(A(x_1,y_1)\) and \(B(x_2,y_2)\) is: 

\(M\left( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2} \right)\)
 
Example Problems
Finding a Dividing Point
  • Given points \(A(2,3)\) and \(B(8,7)\), find the point \(P\) that divides \(AB\) in the ratio \(2:3\).
  • Solution:

\(\begin{aligned} x&=\dfrac{2\times8+3\times2}{2+3}=\dfrac{16+6}{5}=4.4, \\ \\ y&=\dfrac{2\times7+3\times3}{2+3}=\dfrac{14+9}{5}=4.6. \end{aligned}\)

  • Point \(P\) is \((4.4,4.6)\).
Midpoint Calculation
  • Find the midpoint of the line segment joining \((1,2)\) and \((5,6)\).
  • Solution:

\(M\left( \dfrac{1+5}{2},\dfrac{2+6}{2} \right)=(3,4)\).
 
The views expressed in the notes here are those of the contributor and don’t necessarily represent the views of pandai.
Chapter : Coordinate Geometry
Topic : Solve problems involving divisor of a line segment
Form 4 Additional Mathematics
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