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Sagot :
Given:
The directed line segment from (-2, -5) to (7, 10).
A point partitions the segment into a ratio of 2 to 1.
To find:
The coordinates of that point.
Solution:
Section formula: If a point divides a line segment in m:n, then the coordinates of that point are
[tex]Point=\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
The point divides the line segment from (-2, -5) to (7, 10) in 2:1.
Using section formula, we get
[tex]Point=\left(\dfrac{2(7)+1(-2)}{2+1},\dfrac{2(10)+1(-5)}{2+1}\right)[/tex]
[tex]Point=\left(\dfrac{14-2}{3},\dfrac{20-5}{3}\right)[/tex]
[tex]Point=\left(\dfrac{12}{3},\dfrac{15}{3}\right)[/tex]
[tex]Point=\left(4,5\right)[/tex]
Therefore, the coordinates of the partition point are (4,5).
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