Final answer:
The length of segment CD in rectangle ABCD with vertices C(7, -13) and D(11, -10) is calculated using the distance formula, resulting in 5 units.
Step-by-step explanation:
To find the length of segment CD in rectangle ABCD with vertices C(7, -13) and D(11, -10), we can use the distance formula, which is derived from the Pythagorean theorem for calculating the distance between two points in a coordinate plane. The distance formula is: Distance = √[(x2 - x1)² + (y2 - y1)²], where (x1, y1) are the coordinates of the first point and (x2, y2) are the coordinates of the second point.
Applying this formula to our points C and D:
- Let C(7, -13) be (x1, y1) and D(11, -10) be (x2, y2).
- Substitute these values into the distance formula to get:
Distance = √[(11 - 7)² + (-10 + 13)²]
- Calculate the squares: √[(4)² + (3)²]
- Calculate the square roots: √[16 + 9]
- Simplify the square root: √25
- The distance is 5 units.
Therefore, the length of segment CD is 5 units.