Final answer:
The correct coordinates for the point T that is at a distance of x=1 from P(1, 0) on the Cartesian plane are (-4/5, 3/5), as it is the only option that results in a distance of exactly 1 unit when calculated using the distance formula.
Step-by-step explanation:
If the distance from point P(1, 0) to the point T is x, and x = 1, we are looking for a point T that is 1 unit away from P. Since the given options are points on the unit circle (because their coordinates are of the form ± 4/5, ± 3/5, and the square of 4/5 plus the square of 3/5 equals 1), we can find the correct point by checking which of the given options are exactly 1 unit away from P(1, 0).
The distance between two points (x1, y1) and (x2, y2) in the Cartesian plane is given by the formula √((x2 - x1)² + (y2 - y1)²). For each option:
- Option 1: Distance = √((-4/5 - 1)² + (3/5 - 0)²) = √((-9/5)² + (3/5)²) = 1
- Option 2: Distance = √((4/5 - 1)² + (3/5 - 0)²) ≠ 1
- Option 3: Distance = √((-4/5 - 1)² + (-3/5 - 0)²) ≠ 1
- Option 4: Distance = √((4/5 - 1)² + (-3/5 - 0)²) ≠ 1
The only option that gives us a distance of 1 unit is Option 1, so the coordinates for T are (-4/5, 3/5).