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?
someone can help me.
Sure, I can help you with that. To find the coordinate of point Z, we need to set up a proportion using the given ratios.
The ratio of the length of XY segment to the length of YZ segment is given as 5:7. We can set up the proportion as:
XY / YZ = 5 / 7
We know that the length of XY segment is the difference between the coordinates of X and Y, which is 3.8 - 1.3 = 2.5.
Substituting the values into the proportion, we get:
2.5 / YZ = 5 / 7
To find the length of YZ, we can cross-multiply:
2.5 * 7 = 5 * YZ
17.5 = 5 * YZ
Dividing both sides by 5, we find:
YZ = 17.5 / 5 = 3.5
Therefore, the length of YZ segment is 3.5 units.
To find the coordinate of Z, we can subtract the length of YZ from the coordinate of Y:
Z = Y - YZ = 3.8 - 3.5 = 0.3
So, the coordinate of Z is 0.3.
To find the coordinate of Z, we need to use the given ratio of the lengths of the segments XY and YZ.
First, let's find the length of XY. We know that the coordinates of X and Y are 1.3 and 3.8, respectively. Therefore, the length of XY is given by the absolute difference between these two values:
Length of XY = |3.8 - 1.3| = 2.5
Next, let's set up the ratio between the lengths of XY and YZ. We are given that the ratio is 5:7, so we can write:
Length of XY / Length of YZ = 5/7
Substituting the known length of XY (2.5) into the equation:
2.5 / Length of YZ = 5/7
Now, we can solve for the length of YZ by cross-multiplying:
2.5 * 7 = 5 * Length of YZ
17.5 = 5 * Length of YZ
Dividing both sides of the equation by 5:
Length of YZ = 17.5 / 5 = 3.5
Finally, to find the coordinate of Z, we need to add the length of YZ to the coordinate of Y:
Coordinate of Z = Coordinate of Y + Length of YZ
Coordinate of Z = 3.8 + 3.5 = 7.3
Therefore, the coordinate of Z is 7.3.