If UV = X+6 and UY = x - 1 Find YV. Y is the midpoint of U and V. Please show work.
U---V---Y
"Y is the midpoint of U and V."
therefore, UV=VY and UY=2UV=2VY
To find YV, we need to determine the value of UV and UY, and then use the midpoint formula to find YV.
Given: UV = X + 6 and UY = x - 1.
Since Y is the midpoint of U and V, we can set up the equation:
UV = 2 * UY.
Substituting the given values, we get:
X + 6 = 2 * (x - 1).
Now we can solve for x:
X + 6 = 2x - 2.
Add 2 to both sides:
X + 8 = 2x.
Subtract x from both sides:
8 = x.
Now that we have the value of x, we can substitute it back into the original equations to find the values of UV and UY.
For UV:
UV = X + 6 = 8 + 6 = 14.
For UY:
UY = x - 1 = 8 - 1 = 7.
Since Y is the midpoint of U and V, we can use the midpoint formula:
YV = (UV + UY) / 2.
Substituting the values:
YV = (14 + 7) / 2 = 21 / 2 = 10.5.
Therefore, YV = 10.5.