Question

Line segment AB has endpoints at A(-9, 3) and B(1, 8). We want to find the coordinates of point P so that P partitions AB into a part-to-whole ratio of 1:5. Fill in the correct values for the formula below: P =

Answer 1

The coordinates of point P, which partitions line segment AB into a part-to-whole ratio of 1:5, can be found using the formula P = (x₁ + 1/6(x₂ - x₁), y₁ + 1/6(y₂ - y₁)). Therefore, P = (-7, 4).

Step-by-step explanation:

To find the coordinates of point P, which partitions line segment AB into a part-to-whole ratio of 1:5, we can use the formula P = (x₁ + 1/6(x₂ - x₁), y₁ + 1/6(y₂ - y₁)).

In this formula, (x₁, y₁) represents the coordinates of point A (-9, 3), and (x₂, y₂) represents the coordinates of point B (1, 8).

To apply the formula, we first calculate the differences (x₂ - x₁) and (y₂ - y₁), which are (1 - (-9)) = 10 and (8 - 3) = 5, respectively.

Next, we multiply these differences by 1/6, as the part-to-whole ratio is 1:5. 1/6 of 10 is 10/6 or 5/3, and 1/6 of 5 is 5/6.

Finally, we add these scaled differences to the coordinates of point A. Adding 5/3 to -9 gives -9 + 5/3 = -27/3 + 5/3 = -22/3, and adding 5/6 to 3 gives 3 + 5/6 = 18/6 + 5/6 = 23/6.

Therefore, the coordinates of point P are (-22/3, 23/6), which can be simplified to P = (-7, 4).

In conclusion, the coordinates of point P, which partitions line segment AB into a part-to-whole ratio of 1:5, are (-7, 4). This means that P divides the line segment in such a way that the distance between P and A is one-sixth of the distance between A and B, and the distance between P and B is five-sixths of the distance between A and B.