Question

Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 3 with A(6, -10) and B(9, -1).

Answer 1

Explanation:

the answer would be (7,-7)

Answer 2

Explanation:

Use the formulas that allow us to find the point that divides the segment into a ratio which is

`x=(bx_1+ax_2)/(a+b)` and
`y=(by_1+ay_2)/(a+b)` where a is 1 (comes from the ratio) and b is 3 (comes from the ratio as well). Filling in:

`x=(3(9)+1(6))/(1+3)=(27+6)/(4)=(33)/(4)` and then y:

`y=(3(-1)+1(-10))/(1+3)=(-3-10)/(4)=-(13)/(4)` so the coordinates in question are

`((33)/(4),-(13)/(4))`