Question

Find the coordinates of P so that P partitions segment AB in the part-to-whole ratio of 1 to 5 with A(-9, 3) and B(1, 8). Explain.

Find point Z that partitions the directed line segment XY in the ratio of 2:1 where X(1, 2) and Y(7, 5). Explain.

Answer 1

For both problems, we can use the section formula.

1)
`P=\left(((1)(1)+(5)(-9))/(6), ((1)(8)+(5)(3))/(6) \right)=\boxed{\left(-(22)/(3), (23)/(6) \right)}`

2)
`Z=\left(((2)(7)+(1)(1))/(3), (((2)(5)+(1)(2))/(3) \right)=\boxed{(5, 4)}`