Find the coordinates of p so that p partitions the segment ab in the ration 3: 4 if a(-9,9) and b(5,-2)

So contrary to what you may believe, 3:4 is not 3/4 here, but rather "3 equal parts to 4 equal parts", which is a total of 7 equal parts. In short, the question is asking you to put point P 3/7 of the way from A to B (or 4/7 of the way from B to A, but we will do the prior.)

So firstly, how far apart is -9 from 5 (the x-coordinates)? That would be 14 units. Multiply 3/7 by 14:

Next, how far apart is 9 from -2 (the y-coordinates)? That would be 11 units. Multiply 3/7 by 11.

Now, since from -9 to 5 you are increasing, add 6 to -9:

-3 is P's x-coordinate.

Next, since from 9 to -2 you are decreasing, subtract 33/7 from 9.

30/7, or 4 2/7 is P's y-coordinate.

Putting it together, P's coordinate is (-3, 30/7).

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