Answer: (2,3).
Step-by-step explanation:
We need to find the coordinates of the point 1/3 of the way from point P(4,4) to point Q(-2,1).
Let the point be A.
[tex]PA:PQ=1:3[/tex]
[tex]PA:AQ=PA:(PQ-PA)=1:(3-1)=1:2[/tex]
It means the point A divide the segment PQ in 1:2.
Section formula: If a point divide a segment is m:n.
[tex]\left(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\right)[/tex]
[tex]A=\left(\dfrac{1(-2)+2(4)}{1+2},\dfrac{1(1)+2(4)}{1+2}\right)[/tex]
[tex]A=\left(\dfrac{-2+8}{3},\dfrac{1+8}{3}\right)[/tex]
[tex]A=\left(\dfrac{6}{3},\dfrac{9}{3}\right)[/tex]
[tex]A=\left(2,3\right)[/tex]
Therefore, the required coordinates are (2,3).
