Final answer:
The length of the line segment between the points (2,7) and (4,2) is the square root of 29, denoted as √29. Therefore, the length of the line segment is √'29, which is option b.
Step-by-step explanation:
The question asks us to calculate the length of a line segment in an x-y coordinate plane between the points (2,7) and (4,2). To find this length, we can use the distance formula, which is derived from the Pythagorean theorem:
d = √((x2 - x1)² + (y2 - y1)²)
Substituting the given points into the distance formula:
d = √((4 - 2)² + (2 - 7)²)
d = √((2)² + (-5)²)
d = √(4 + 25)
d = √29
Therefore, the length of the line segment is √29.
The length of a line segment in an x-y coordinate plane can be found using the distance formula. The formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates of the points are (2,7) and (4,2). Plugging these values into the formula, we get:
d = sqrt((4 - 2)^2 + (2 - 7)^2) = sqrt(2^2 + (-5)^2) = sqrt(4 + 25) = sqrt(29).
Therefore, the length of the line segment is √'29, which is option b.