Final answer:
The length of segment AB with endpoints A(-1,7) and B(11,-1) is calculated using the distance formula and is approximately 14.4 units when rounded to one decimal place.
Step-by-step explanation:
To find the length of segment AB with endpoints A(-1,7) and B(11,-1), we use the distance formula derived from the Pythagorean theorem. The distance formula is √((x2-x1)² + (y2-y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points.
The calculation for the length of segment AB is as follows:
First, subtract the x-coordinate of point A from the x-coordinate of point B: 11 - (-1) = 12.
Next, subtract the y-coordinate of point A from the y-coordinate of point B: -1 - 7 = -8.
Now, square each of the differences: 12² = 144 and (-8)² = 64.
Add the squared differences: 144 + 64 = 208.
Take the square root of the sum: √208 ≈ 14.422.
Therefore, the length of segment AB, rounded to one decimal place, is 14.4 units.