Points X and Y are on a number line, and Y partitions XZ segment into two parts so that the of the length of XY segment to the length of YZ segment is 5:7. The coordinate of x is 1.3, and the coordinate of Y is 3.8. What is the coordinate of Z?
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To find the coordinate of point Z, we can use the given information about the ratios of segment lengths.
Given: The length ratio of XY to YZ is 5:7.
First, let's calculate the length of XY using the coordinates of X and Y. The length of XY can be found by taking the absolute difference between the coordinates of X and Y:
Length of XY = |x - y| = |1.3 - 3.8| = |-2.5| = 2.5
We know that the length of XY is represented by the ratio 5 in the given proportion. So, we can set up a proportion:
Length of XY / Length of YZ = 5 / 7
Plugging in the length of XY, we have:
2.5 / Length of YZ = 5 / 7
Now, let's solve for the Length of YZ:
2.5 * 7 = 5 * Length of YZ
17.5 = 5 * Length of YZ
Length of YZ = 17.5 / 5
Length of YZ = 3.5
To find the coordinate of point Z, we need to determine its position relative to point Y. Since point Y is at a coordinate of 3.8, we need to subtract the length of YZ from the coordinate of Y:
Coordinate of Z = Coordinate of Y - Length of YZ
Coordinate of Z = 3.8 - 3.5
Coordinate of Z = 0.3
Therefore, the coordinate of point Z is 0.3.
To find the coordinate of Z, we need to determine the length of the XZ segment and the YZ segment.
Given that the ratio of the length of XY segment to the length of YZ segment is 5:7, we can write the equation:
XY / YZ = 5 / 7
Let's calculate the length of XY:
XY = Y - X
XY = 3.8 - 1.3
XY = 2.5
Now we can set up the equation using the lengths:
2.5 / YZ = 5 / 7
To solve for YZ, cross multiply:
2.5 * 7 = 5 * YZ
17.5 = 5 * YZ
Divide both sides by 5:
YZ = 17.5 / 5
YZ = 3.5
Finally, to find the coordinate of Z, we add the length of YZ to the coordinate of Y:
Z = Y + YZ
Z = 3.8 + 3.5
Z = 7.3
Therefore, the coordinate of Z is 7.3.