Points X and Z are on a number line, and point Y partitions line XZ into two parts so that the ratio of the length of line segment XY to the length of line segment YZ is 3:5. The coordinate of X is 0.4, and the coordinate of Y is 2.7. What is the coordinate of Z? Show all work.
3 + 5 = 8
so ratio of xz to xy is 8/3
but xy is 2.7 - 0.4 = 2.3
so xz = (8/3)2.3 = 6.13
so z is at 0.4 + 6.13 = 6.53
XY/YZ = 3/5
(2.7-0.4)/YZ = 3/5
YZ = 3.83
Z = Y + 3.83 = 2.7 + 3.83 = 6.53
To find the coordinate of point Z, we can use the ratio of the lengths of line segment XY to line segment YZ.
Given:
Coordinate of X = 0.4
Coordinate of Y = 2.7
Let's assume the coordinate of Z as z.
We know that the ratio of XY to YZ is 3:5, which means the length of XY is 3/8th of the total length (since 3 + 5 = 8) and the length of YZ is 5/8th of the total length.
The total length of XZ can be found by subtracting the coordinate of X from the coordinate of Y:
Total length (XZ) = (Coordinate of Y) - (Coordinate of X)
= 2.7 - 0.4
= 2.3
Now, we can calculate the lengths of XY and YZ.
Length of XY = (3/8) * (Total length)
= (3/8) * 2.3
= 0.8625
Length of YZ = (5/8) * (Total length)
= (5/8) * 2.3
= 1.4375
Since point X is at coordinate 0.4, to find the coordinate of Z, we need to add the length of YZ to the coordinate of X:
Coordinate of Z = (Coordinate of X) + (Length of YZ)
= 0.4 + 1.4375
= 1.8375
Therefore, the coordinate of point Z is 1.8375.