Find the coordinates of the point on the directed segment from (3,2) to (6,8) that divides into a ratio of 1: 3.a. (4.5, 5.5)b. (5.25, 6.25)c. (3.75, 3.5)d. (4,4)

c. (3.75, 3.5)

Step-by-step explanation:

Let's call the given segment AB, and the dividing point P. Then you want AP:PB = 1:3.

There are a couple of ways you can get there.

1. Recognize that when you subtract the coordinates of A from P, the difference will be 1/4 of the result of subtracting A from B. That is, ...

P-A = (1/(1+3))·(B-A)

We can see that B-A = (6,8) -(3,2) = (3, 6), so 1/4 of that is (3/4, 3/2) = (0.75, 1.5). Adding these values to the coordinates of A gives ...

P = A + (.75, 1.5) = (3.75, 3.5)

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2. Finish working out the equation above to solve for P:

4(P -A) = B -A

4P = B + 3A

P = (3A + B)/4 . . . . . note the multiplier for A is the relative length of PB and vice versa

P = (3(3, 2) +(6, 8))/4 = (15/4, 14/4) = (3.75, 3.5)

Comment on choosing an answer

You only need to determine one of the coordinates in order to pick the correct answer. Finding both coordinates can help give you assurance that you have worked it out correctly.

x = 3 ± √(5+y)

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