What are the coordinates of the point that is 1/6 of the way from a(14,-1) to b(-4,23)?

a. (8,6)

b. (5,11)

c. (-1,19)

d. (11,3)

D. (11,3)

First of all, let's plot each point as indicated in figure below. To find the point that divide a segment with endpoints and a ratio:

We must use the formula:

To find the ratio, we know that:

because is 1/6 of the way from to

So the other part of the segment is:

Therefore, the ratio can be found as:

From here, we can calculate the point we are looking for:

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answer for #1 is c

answer for #2 is d

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