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Question 1106556: Find the coordinates of point P that divides the segments with the given endpoints in the ratio 2 : 3.
i A(-3, -1) and B(2, 4) iii A(-2, -3) and B(4, 0)
ii A(-4, 9) and B(1, -1) iv A(-6, -1) and B(3, 8)
Found 2 solutions by stanbon, greenestamps:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the coordinates of point P that divides the segments with the given endpoints in the ratio 2 : 3.
i A(-3, -1) and B(2, 4)
d(A to B) = sqrt[(2--3)^2 + (4--1)^2] = sqrt[25+25] = 25sqrt(2)
P = (-3+(2/3)25sqrt(2),-1+(2/3)25sqrt(2))
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ii A(-4, 9) and B(1, -1)
d(A to B) = sqrt[(1--4)^2+(-1-9)^2] = sqrt[25+100] = 5sqrt(5)
P = (-4+(2/3)5*sqrt(5),9+(2/3)5sqrt(5))
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etc.
Cheers,
Stan H.
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iii A(-2, -3) and B(4, 0)
iv A(-6, -1) and B(3, 8)
Answer by greenestamps(13209)  (Show Source):
You can put this solution on YOUR website!
The solution by the first tutor is wrong.
Adding 2/3 of the distance between the two endpoints to each of the x and y coordinates of the first endpoint does not give you the coordinates of point P.
Furthermore, if P divides segment AB into two parts in the ratio 2:3, then point P is 2/5 of the distance from A to B -- not 2/3 of the distance.
To find the coordinates of point P in each case, it is much easier to work with the x and y components separately, rather than working with the distance between the endpoints.
i) A(-3,-1) and B(2,4)
The difference in the x coordinates is 5; the difference in the y coordinates is also 5. 2/5 of 5 is 2; so point P is 2 units in the x direction and 2 units in the y direction from A, giving you P(-1,1).
ii) A(-2,-3) and B(4,0)
The difference in the x coordinates is 6; the difference in the y coordinates is 3. 2/5 of 6 is 2.4; 2/5 of 3 is 1.2; so point P is 2.4 units in the x direction and 1.2 units in the y direction from A, giving you P(0.4,-1.8).
The other two cases are worked in the same way....
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