Question

Directed line segment porque is shown on the coordinate plane. What are the coordinates of the point 1/3 of the way from point P(4,4) to point Q(-2,1)?

Answer 1

Answer: (2,3).

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.

`PA:PQ=1:3`

`PA:AQ=PA:(PQ-PA)=1:(3-1)=1:2`

It means the point A divide the segment PQ in 1:2.

Section formula: If a point divide a segment is m:n.

`\left((mx_2+nx_1)/(m+n),(my_2+ny_1)/(m+n)\right)`

`A=\left((1(-2)+2(4))/(1+2),(1(1)+2(4))/(1+2)\right)`

`A=\left((-2+8)/(3),(1+8)/(3)\right)`

`A=\left((6)/(3),(9)/(3)\right)`

`A=\left(2,3\right)`

Therefore, the required coordinates are (2,3).