Question 1106556
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The solution by the first tutor is wrong.<br>
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.<br>
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.<br>
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.<br>
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).<br>
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).<br>
The other two cases are worked in the same way....