Final answer:
Using the distance formula for the coordinates (19, 5) and (x, -3), we find two possible values of x to be 34 and 4, which match neither of the given options a) 35, b) -15, c) 53, d) 2.
Step-by-step explanation:
The distance between two points (19, 5) and (x, -3) is given as 17. To find the value(s) of x that satisfy this condition, we can use the distance formula for two points in a coordinate plane:
Distance = √[(x2 - x1)² + (y2 - y1)²]
Plugging in the given points and distance:
17 = √[(x - 19)² + (-3 - 5)²]
289 = (x - 19)² + 64
(x - 19)² = 225
x - 19 = ±15
Therefore, x can be either 19 + 15 or 19 - 15.
x = 34 or x = 4
However, none of the provided options match these results. Thus, there seems to be a mistake in the question or the given choices.