Final answer:
To approximate the distance between the points (-1,1) and (7,4), the distance formula is used and the result is approximately 8.5 units to the nearest tenth.
Step-by-step explanation:
To approximate the distance between the points (-1,1) and (7,4) to the nearest tenth, we use the distance formula derived from the Pythagorean theorem:
Distance = √((x2 - x1)^2 + (y2 - y1)^2).
Here, (x1, y1) = (-1, 1) and (x2, y2) = (7, 4). We substitute these values into the formula:
Distance = √((7 - (-1))^2 + (4 - 1)^2)
Distance = √((8)^2 + (3)^2)
Distance = √(64 + 9)
Distance = √(73)
Using a calculator, we find that the distance is approximately 8.5 to the nearest tenth.