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Part 1
On a number​ line, the coordinates of​ X, Y,​ Z, and W are negative 6−6​, negative 2−2​, 22​, and 66​, respectively. Find the lengths of the two segments below. Then tell whether they are congruent.
XY overbarXY and ZW overbarZW
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Part 1
The length of XY overbarXY is 44. ​(Type an integer or a​ decimal.)
The length of ZW overbarZW is 44. ​(Type an integer or a​ decimal.)
Part 2
Are the segments XY overbarXY and ZW overbarZW ​congruent?

1 answer

To find the lengths of the segments \( \overline{XY} \) and \( \overline{ZW} \), we calculate the distance between the points.

Part 1: Lengths of the Segments

  1. Length of \( \overline{XY} \):

    • Coordinates: \( X = -6 \) and \( Y = -2 \)
    • Length calculation: \[ |X - Y| = |-6 - (-2)| = |-6 + 2| = |-4| = 4 \]

  2. Length of \( \overline{ZW} \):

    • Coordinates: \( Z = 2 \) and \( W = 6 \)
    • Length calculation: \[ |Z - W| = |2 - 6| = |-4| = 4 \]

Thus, the lengths of the segments are:

  • The length of \( \overline{XY} \) is \( 4 \).
  • The length of \( \overline{ZW} \) is \( 4 \).

Part 2: Congruency of the Segments

Two segments are congruent if they have the same length. Since both lengths are equal:

\[ 4 = 4 \]

Conclusion: Yes, the segments \( \overline{XY} \) and \( \overline{ZW} \) are congruent.

Summary

  • Length of \( \overline{XY} \) = 4
  • Length of \( \overline{ZW} \) = 4
  • Are the segments congruent? Yes.