Final answer:
The distance between the points (2, -9) and (-1, 4) is calculated using the Pythagorean theorem for the coordinate plane, resulting in approximately 13.4 units when rounded to the nearest tenth.
Step-by-step explanation:
To find the distance between the two points (2, -9) and (-1, 4), we utilize the Pythagorean theorem applied to the coordinate plane. This involves calculating the differences between the x-coordinates and the y-coordinates of the points, squaring those differences, adding the squares together, and then taking the square root of the resulting sum. We use the following distance formula for points (x1, y1) and (x2, y2):
d = √[(x2 - x1)² + (y2 - y1)²]
For (2, -9) and (-1, 4), the calculation would be:
d = √[(-1 - 2)² + (4 - (-9))²]
d = √[(-3)² + (13)²]
d = √[9 + 169]
d = √178
d ≈ 13.3 (rounded to the nearest tenth)
Therefore, the correct answer is B) 13.4 units, rounded to the nearest tenth of a unit.