Final answer:
To find the value of x, we can use the midpoint formula which is 16/9.
Step-by-step explanation:
To find the value of x, we can use the midpoint formula. According to the formula, the x-coordinate of the midpoint is the average of the x-coordinates of the two endpoints, and the same applies to the y-coordinate.
Given that XP = 8x - 2 and PY = 12x - 30, we can set up the equation:
(8x - 2 + 12x - 30) / 2 = x
Simplifying the equation, we get:
(20x - 32) / 2 = x
Multiplying both sides of the equation by 2 to eliminate the fraction, we get:
20x - 32 = 2x
20x - 2x = 32
18x = 32
x = 32/18
x = 16/9