The following table shows points on a numberline and their co-ordinates. Decide whether the pair of segments given below the table are congruent or not.
`{:("Point"," L","M","N"," P","Q",R),("Co-ordinate",-5,0,8,-1,7,4):}`
seg QR and seg LM.

Answer

To determine whether the segments QR and LM are congruent, we will calculate the lengths of both segments using their coordinates.

### Step 1: Identify the coordinates of points Q and R
- The coordinates are given as:
- Q = 7
- R = 4

### Step 2: Calculate the length of segment QR
- The length of segment QR can be calculated using the formula:
\[ \text{Length of } QR = |Q - R| = |7 - 4| = |3| = 3 \]

### Step 3: Identify the coordinates of points L and M
- The coordinates are given as:
- L = -5
- M = 0

### Step 4: Calculate the length of segment LM
- The length of segment LM can be calculated using the formula:
\[ \text{Length of } LM = |L - M| = |-5 - 0| = |-5| = 5 \]

### Step 5: Compare the lengths of segments QR and LM
- We found that:
- Length of QR = 3
- Length of LM = 5

Since the lengths of segments QR and LM are not equal, we conclude that the segments are not congruent.

### Final Conclusion
- Therefore, segments QR and LM are not congruent.

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