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.

Question

XY overbarXY and ZW overbarZW
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Part 1
The length of XY overbarXY is enter your response here. ​(Type an integer or a​ decimal.)
The length of ZW overbarZW is enter your response here. ​(Type an integer or a​ decimal.)

Answer 1

To find the lengths of the segments \( \overline{XY} \) and \( \overline{ZW} \), we will use the distance formula for points on a number line, which is simply the absolute difference between the coordinates.

1. Finding the length of \( \overline{XY} \):

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

2. Finding the length of \( \overline{ZW} \):

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

Now we have:

• Length of \( \overline{XY} = 4 \)
• Length of \( \overline{ZW} = 4 \)

Conclusion:

The lengths of \( \overline{XY} \) and \( \overline{ZW} \) are both 4, so they are congruent.

Thus, you can fill in the responses as follows:

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

Since both lengths are equal, they are indeed congruent.