Final answer:
To find the length of line XY, the midpoint formula was used to calculate the coordinates of Y, and then the distance formula was applied to find the distance between X and Y to be approximately 5.83, and the closest answer choice is 6.
Step-by-step explanation:
The student asked: If point Y is the midpoint of a segment that contains the points X (-1, 8) and Z (5, -2), what is the length of line XY?
To find the coordinates of the midpoint Y, we use the midpoint formula which is given by:
- Midpoint Y = ((x1 + x2)/2, (y1 + y2)/2)
Substituting the given coordinates of X and Z, we get:
- Midpoint Y = ((-1 + 5)/2, (8 + (-2))/2) = (2, 3)
To find the distance XY, we use the distance formula:
- Distance = √((x2 - x1)² + (y2 - y1)²)
Substituting X(-1, 8) and Y(2, 3), we calculate:
- Distance XY = √((2 - (-1))² + (3 - 8)²)
- Distance XY = √((3)² + (-5)²)
- Distance XY = √(9 + 25)
- Distance XY = √34
As √34 is approximately 5.83, the closest option to this value would be 6 (Option a).