Question

A segment has endpoint X (- 10,0) and Y (-2,6)

Answer 1

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)**