Points X and Z are on a number line, and point Y partitions XZ into two parts so that the ratio of the length of XY to the length of YZ is 4 : 5.

The coordinate of X is 3.8, and the coordinate of Y is 7.9.
What is the coordinate of Z?

Make your sketch, let Z be x

then :
(x-7.9)/(7.9-3.8) = 5/4
(x-7.9)/4.1 = 5/4

cross-multiply and solve for x

To find the coordinate of point Z, we need to determine the length of YZ and then subtract it from the coordinate of Y.

Given that the ratio of the length of XY to YZ is 4:5, we can set up the following proportion:

XY / YZ = 4 / 5

We know that the length of XY is the difference between the coordinates of X and Y, which is:

XY = Y - X

Substituting the given coordinates:

XY = 7.9 - 3.8 = 4.1

Now, let's solve for YZ by rearranging the proportion:

XY / YZ = 4 / 5

4.1 / YZ = 4 / 5

Cross-multiplying:

4.1 * 5 = 4 * YZ

20.5 = 4 * YZ

Dividing by 4:

YZ = 20.5 / 4

YZ = 5.125

Finally, we can find the coordinate of point Z by subtracting the length YZ from the coordinate of Y:

Z = Y - YZ

Z = 7.9 - 5.125

Z ≈ 2.775

Therefore, the coordinate of point Z is approximately 2.775.