Given a line segment A(16, 8) and B(1, 3) what are the coordinates or the line segment partitioned two-fifths from A to B.

1 answer:

7 0

Partitioning means to find the dividing point between two points.
This is done by prorating the difference in x- and y-coordinates, and adding to the first.

We will take the first point (from A to B) as A(16,8).
The difference is B-A, i.e.
(1,3)-(16,8) = (-15,-5)
2/5 of the difference is (2/5)*(-15,-5) = (-6,-2)
Add the difference to the first coordinates (point A) gives
Point of division = (16,8)+(-6,-2) = (16-6, 8-2) = (10,6)

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This question is incomplete, in that the Excel File: data07-11.xlsx a. was not provided, but I was able to get the information on the Excel File: data07-11.xlsx a. from google as below:

57 61 86 74 72 73

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The image of the Excel File: data07-11.xlsx a. is also attached below.

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a) Point estimate of sample mean = 68

b) Point estimate of standard deviation (4 decimals) = 17.8122

Step-by-step explanation:

a) Point estimate of sample mean, \bar{x} = ∑Xi / n = (57 + 61 + 85 + 74 + 73 + 72 + 20 + 58 + 81 + 78 + 84 + 73)/12 = 68

b) Point estimate of standard deviation = sqrt ∑ Xi² - n\bar{x}² / n-1)

= sqrt(((57 - 68)^2 + (61 - 68)^2 + (85 - 68)^2 + (74 - 68)^2 + (73 - 68)^2 + (72 - 68)^2 + (20 - 68)^2 + (58 - 68)^2 + (81 - 68)^2 + (78 - 68)^2 + (84 - 68)^2 + (73 - 68)^2)/11) = 17.8122