Question

What are the coordinates of the point on the directed line segment from (4, -1)(4,−1) to (10, 8)(10,8) that partitions the segment into a ratio of 2 to 1?

Answer 1

`C(x,y) = (8,5)`

Explanation:

Given

`A(x_1,y_1) = (4,1)`

`B(x_2,y_2) = (10,8)`

Required

Partition into 2:1

Here, we'll make use of the following formula:

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

Where

`m:n = 2:1`

Substitute values for m,n,x1,x2,y1 and y2

`C(x,y) = ((1 * 4 + 2 * 10)/(1 + 2),(1 * -1 + 2 * 8)/(1 + 2))`

`C(x,y) = ((24)/(3),(15)/(3))`

`C(x,y) = (8,5)`