Question

Directed line segment has endpoints P(– 8, – 4) and Q(4, 12). Determine the point that partitions the directed line segment in a ratio of 3:1.

Answer 1

Explanation:

1,8

Answer 2

Point (1,8)

Explanation:

We will use segment formula to find the coordinates of point that will partition our line segment PQ in a ratio 3:1.

When a point divides any segment internally in the ratio m:n, the formula is:

`[x=(mx_2+nx_1)/(m+n),y= (my_2+ny_1)/(m+n)]`

Let us substitute coordinates of point P and Q as:

`x_1=-8`,

`y_1=-4`

`x_2=4`

`y_2=12`

`m=3`

`n=1`

`[x=((3*4)+(1*-8))/(3+1),y=((3*12)+(1*-4))/(3+1)]`

`[x=(12-8)/(4),y=(36-4)/(4)]`

`[x=(4)/(4),y=(32)/(4)]`

`[x=1,y=8]`

Therefore, point (1,8) will partition the directed line segment PQ in a ratio 3:1.