Step-by-step explanation:
does that mean you understand all the other questions but not 5. ?
that is strange, as this seems to be the easiest one of all the 6 questions.
to be sure, let's have a look at all 6.
1.
the distance MJ = 18 - 2 = 16
MX / XJ = 3/1
the ratio talkes about 3+1 = 4 basic units.
as the whole distance is 16, one such basic ratio unit is 16/4 = 4.
that means from M to X we have 3 of these basic ratio units, and from X to J the remaining 1 of the basic ratio units.
so, MX = 3×4 = 12
since M = 2, X = 2 + 12 = 14
2.
similar to 1.
just now
MY / YJ = 2/3
so, the ratio uses 2+3 = 5 basic units.
that means 1 basic unit is 16/5 = 3.2
2 basic units = 2 × 3.2 = 6.4
3 basic units = 3 × 3.2 = 9.6
so, MY = 6.4
since M = 2, Y = 2 + 6.4 = 8.4
3.
the distance A F = 5 - -7 = 5 + 7 = 12
AW / WF = 1/3
so, the ratio uses 1+3 = 4 basic units.
1 basic unit is 12/4 = 3
3 basic units is 3 × 3 = 9
so, AW = 3
since A = -7, W = -7 + 3 = -4
4.
the distance BF = 5 - -5 = 5 + 5 = 10
BX / XF = 3/2
so, the ratio uses 3+2 = 5 basic units.
1 basic unit = 10/5 = 2
2 basic units = 2 × 2 = 4
3 basic units = 3 × 2 = 6
so, BX = 6
since B = -5, X = -5 + 6 = 1
5.
the distance CE = 2 - -4 = 2 + 4 = 6
CY / YE = 1/1
so, the ratio uses 1+1 = 2 basic units.
1 basic unit = 6/2 = 3
so, CY = 3
since C = -4. Y = -4 + 3 = -1
6.
attention : this goes in the other direction than the other questions. all the others were looking from a point on the left to a point on the right.
but this one looks from a point on the right to a point on the left.
but the same principles apply.
the distance FD = |1 - 5| = |-4| = 4
a distance is always positive, so for this direction we need to apply the absolute value (formality we did that also for the other direction in the other questions, but there it was not necessary to use it explicitly) .
FZ / ZD = 5/3
so, the ratio uses 5+3 = 8 basic units.
1 basic unit = 4/8 = 0.5
3 basic units = 3 × 0.5 = 1.5
5 basic units = 5 × 0.5 = 2.5
so, FZ = 2.5
since F = 5, Z = 5 - 2.5 = 2.5
this is where the other direction really hits : since we have to go to the smaller side, we have to subtract the distance from the original coordinate (instead of the usual addition).
![[4^{(2-5)}].[g^{(3-12)}].[p^{-2}].[m^{5}]](https://tex.z-dn.net/?f=%5B4%5E%7B%282-5%29%7D%5D.%5Bg%5E%7B%283-12%29%7D%5D.%5Bp%5E%7B-2%7D%5D.%5Bm%5E%7B5%7D%5D)
![[4^{-3}].[g^{-9}].[p^{-2}].[m^{5}]](https://tex.z-dn.net/?f=%5B4%5E%7B-3%7D%5D.%5Bg%5E%7B-9%7D%5D.%5Bp%5E%7B-2%7D%5D.%5Bm%5E%7B5%7D%5D)
or 