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.

b. Fill in the correct values for the formula below:

P = (
+
(
-
),
+
(
-
)

Answer 1

To find the coordinates of point P that partitions AB into a ratio of 1:5, we need to calculate the distance between points A and B. Then, we can use the distance ratio to find the length of the shorter part of AB and finally determine the coordinates of point P using the formula.

Step-by-step explanation:

Step 1:

Find the distance between points A and B using the distance formula: sqrt((x2 - x1)^2 + (y2 - y1)^2)

Distance AB = sqrt((1 - -9)^2 + (8 - 3)^2) = sqrt(10^2 + 5^2) = sqrt(100 + 25) = sqrt(125)

Distance AB = sqrt(125) ≈ 11.18 units

Step 2:

Calculate the length of the shorter part of AB by dividing the total distance by the sum of the ratio parts: AB/(1 + 5) = 11.18/6 ≈ 1.86 units.

Step 3:

Find the coordinates of point P using the formula:

P = ((1-(-9))/(1+5) * (1.86), (8-3)/(1+5) * (1.86))

P = (10/6 * 1.86, 5/6 * 1.86)

P = (3.1, 1.55)