Final answer:
To determine the coordinates of point T at distance x from point P(1, 0), we use the distance formula for each of the given coordinate pairs to identify which pair yields the distance x.
Step-by-step explanation:
The question requires the determination of the coordinates of a point T that is distance x away from point P(1, 0) on a two-dimensional plane. Given a set of possible coordinates for the point T, we need to identify which coordinate pairs would be exactly x units away from point P. The distance between two points (x1, y1) and (x2, y2) in a Cartesian coordinate system is given by the formula √((x2 - x1)² + (y2 - y1)²). To find if the given coordinates (4/5, -3/5), (-4/5, 3/5), (4/5, 3/5), and (-4/5,-3/5) are at distance x from point P(1, 0), we calculate the distance using the formula for each pair.
For instance, to find the distance from P to the point (4/5, -3/5), we substitute and get:
Distance = √((4/5 - 1)² + (-3/5 - 0)²) = √((-1/5)² + (-3/5)²) = √((1/25) + (9/25)) = √(10/25) = √(2/5) = √(0.4). If √(0.4) is equal to the distance x, then (4/5, -3/5) could be the correct coordinates. The same process is applied to the other coordinates to find the matching distance x.