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? Help help
To find the coordinate of Z, we need to determine the length of the XY and YZ segments and apply that information to find the position of Z on the number line.
Given:
- Coordinate of X = 1.3
- Coordinate of Y = 3.8
Step 1: Find the length of XY segment
To find the length of XY, we subtract the coordinates of X and Y:
Length of XY = Y coordinate - X coordinate = 3.8 - 1.3 = 2.5
Step 2: Find the length of YZ segment
The ratio of the length of XY to the length of YZ is given as 5:7. Therefore, we can set up the following equation:
Length of XY / Length of YZ = 5 / 7
Substituting the known values, we can solve for the length of YZ:
2.5 / Length of YZ = 5 / 7
Cross multiplying, we get:
2.5 * 7 = 5 * Length of YZ
17.5 = 5 * Length of YZ
Now, divide both sides of the equation by 5 to solve for the Length of YZ:
Length of YZ = 17.5 / 5 = 3.5
Step 3: Find the coordinate of Z
To find the coordinate of Z, we add the length of YZ to the coordinate of Y:
Coordinate of Z = Y coordinate + Length of YZ = 3.8 + 3.5 = 7.3
Therefore, the coordinate of Z is 7.3 on the number line.