Final answer:
The length of line segment CD with endpoints C (5, -7) and D (3, -4) is calculated using the distance formula, resulting in √[13], an irrational number that can be approximated with a calculator.
Step-by-step explanation:
To find the length of line segment CD given the endpoints C (5, -7) and D (3, -4), we can use the distance formula derived from the Pythagorean theorem, which works for any two points in a Cartesian coordinate system.
The formula is given by:
d = √[(x2 - x1)^2 + (y2 - y1)^2]
Plugging in the coordinates of C and D into the formula, we get:
d = √[(3 - 5)^2 + (-4 + 7)^2] = √[(-2)^2 + (3)^2] = √[4 + 9] = √[13]
Therefore, the length of line segment CD is √[13], which is an irrational number and can be approximated using a calculator.
To find the length of line segment CD with endpoints C(5, -7) and D(3, -4), we can use the distance formula. The distance formula is sqrt((x2 - x1)^2 + (y2 - y1)^2). Plugging in the values from the endpoints, we have sqrt((3 - 5)^2 + (-4 - (-7))^2). Simplifying this, we get sqrt((-2)^2 + (3)^2), which is sqrt(4 + 9) = sqrt(13).