Given:
A(16, 4)
B(34, 40)
Line segment AB partition in the ratio 1 : 5.
To find:
The coordinate of a point that partitions AB.
Solution:
Section formula:
[tex]$P(x,y)=\left(\frac{m x_{2}+n x_{1}}{m+n}, \frac{m y_{2}+m y_{1}}{m+n}\right)[/tex]
Here [tex]x_1=16, y_1=4, x_2=34, y_2=40[/tex] and m = 1, n = 5
[tex]$P(x,y)=\left(\frac{1\times 34+5 \times 16}{1+5}, \frac{1\times 40+5 \times4}{1+5}\right)[/tex]
[tex]$P(x,y)=\left(\frac{ 34+80}{6}, \frac{40+20}{6}\right)[/tex]
[tex]$P(x,y)=\left(\frac{ 114}{6}, \frac{60}{6}\right)[/tex]
[tex]$P(x,y)=(19, 10)[/tex]
The coordinate of point that partitions the segment AB is (19, 10).
