Final answer:
To find the value of TU, we need to use the midpoint formula to set up an equation and solve for x. Once we find the value of x, we can substitute it back into the equation to calculate the value of TU. In this case, TU is equal to 14.
Step-by-step explanation:
To find the value of TU, we need to first find the value of ST and SU. Let's set up an equation using the midpoint formula: Midpoint = (ST + SU) / 2
Since the point is the midpoint, we can substitute the values of ST and SU into the equation: (4x-3 + 7x+1) / 2 = TU
Simplifying the equation: (11x-2) / 2 = TU
To find the value of x, we equate the midpoint equation with the given value of the midpoint: (11x-2) / 2 = 14
Multiplying both sides of the equation by 2: 11x-2 = 28
Adding 2 to both sides: 11x = 30
Dividing both sides by 11: x = 30/11
Substituting the value of x back into the midpoint equation: TU = (11(30/11)-2) / 2
Calculating the value of TU: TU = 28/2 = 14