Point of partition refers that a point intersect a particular line or curve at a fixed ratio. The coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4) is (3.5,7).
Given information-
The coordinates of the A is (5,8).
The coordinates of the B is (-1,4).
P partitions the segment AB in the ratio 1:3.
Point of Partition
Point of partition refers that a point intersect a particular line or curve at a fixed ratio.
When a point [tex]p(x,y)[/tex] intersect a line which has the coordinates [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] at a ratio l and m then this point can be represent as,
[tex]p(x,y)=\left ( \dfrac{lx_2+mx_1}{l+m} , \dfrac{ly_2+my_1}{l+m} \right )[/tex]
Put the values,
[tex]p(x,y)=\left ( \dfrac{1\times(-1)+3\times 5}{1+3} , \dfrac{1\times 4+3\times8}{1+3} \right )[/tex]
[tex]p(x,y)=\left ( \dfrac{-1+15}{4} , \dfrac{4+24}{4} \right )[/tex]
[tex]p(x,y)=\left ( \dfrac{14}{4} , \dfrac{28}{4} \right )[/tex]
[tex]p(x,y)=(3.5,7)[/tex]
Hence the coordinates of P so that P partitions the segment AB in the ratio 1:3 if A(5,8) and B(−1,4) is (3.5,7).
Learn more about the point of partitions of a line here;
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