Final answer:
The length of segment CD is found using the distance formula. After calculating the differences in x and y coordinates, their squares, and the sum, the length is √40, which simplifies to 2√10.
Step-by-step explanation:
To find the length of segment CD in simplest radical form, we will use the distance formula, which is derived from the Pythagorean theorem and used for finding the distance between two points in a two-dimensional space.
The distance formula is √((x2 - x1)² + (y2 - y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, point C is at (-4,9) and point D is at (2,7).
Applying the distance formula:
- Find the difference in x-coordinates: (2 - (-4)) = 6
- Find the difference in y-coordinates: (7 - 9) = -2
- Square these differences: 6² = 36, (-2)² = 4
- Add the squares: 36 + 4 = 40
- Take the square root of the sum: √40
The length of segment CD, in simplest radical form, is √40 or 2√10.