Points A and B define a segment on the number line. This segment starts at 0 and ends at the 84 tick on the number line.
That tells us that the segment has a length of 84 (the difference between 84 and 0 ; 84-0 = 84)
now, there is a partition of the line segment in a quotient 9:7
That means that the partition was made so as to leave 9 sections to the left (between 0 and the point P) and 7 of the same size sections to the right of P towards point B.
So let's think about a total of 9 divisions on the left and 7 divisions on the right of point P. That is, a total of 9 + 7 = 16 divisions of our segment AB.
So, what is the length of each of these divisions?
We need to divide 84 (the length of segment AB) in 16 parts:
84/16 = 5.25
5.25 is the length of each of the divisions we want.
Now, recall that point P is located 9 of these divisions to the right of point A,
then we need to add 9 of the 5.25 length divisions to point A (located at zero) to mark that point P.
This means that point P is at position:
0 + 9 times 5.25 = 0 + 47.25 = 47.25
P is located at the point 47.25 on the number line