To analyze the segment with endpoints \( X(-10, 0) \) and \( Y(-2, 6) \), we can calculate several properties, such as the length of the segment and the midpoint.
Length of the Segment
The length of the segment can be calculated using the distance formula, which is given by:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Here, \( (x_1, y_1) = (-10, 0) \) and \( (x_2, y_2) = (-2, 6) \).
Substituting the coordinates into the formula:
\[ d = \sqrt{((-2) - (-10))^2 + (6 - 0)^2} \] \[ d = \sqrt{(-2 + 10)^2 + (6 - 0)^2} \] \[ d = \sqrt{(8)^2 + (6)^2} \] \[ d = \sqrt{64 + 36} \] \[ d = \sqrt{100} \] \[ d = 10 \]
Thus, the length of the segment \( XY \) is 10 units.
Midpoint of the Segment
The midpoint \( M \) of a segment with endpoints \( (x_1, y_1) \) and \( (x_2, y_2) \) can be calculated using the formula:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Substituting the coordinates of points \( X \) and \( Y \):
\[ M = \left( \frac{-10 + (-2)}{2}, \frac{0 + 6}{2} \right) \] \[ M = \left( \frac{-12}{2}, \frac{6}{2} \right) \] \[ M = (-6, 3) \]
The midpoint of the segment \( XY \) is (-6, 3).
Summary
- Length of segment \( XY \): 10 units
- Midpoint of segment \( XY \): (-6, 3)