Question

On a number line, A is at 0 and B is at 84. Point P partitions line segment AB in a 9:7 ratio. What is thelocation of point P? Round to the nearest hundredth if necessary.

Answer 1

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