NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 9: Symmetry and Practical Geometry - Fill in the Blanks
Question 25

Question. 25

In Fig. 9.10, if B is the image of the point A with respect to the line \(l\) and P is any point lying on \(l\), then the lengths of line segments PA and PB are _____.

Fig 9.10

Answer:

equal.

Detailed Answer with Explanation:

  1. The line \(l\) works like a mirror.
  2. Point A has its mirror image at point B with respect to the line \(l\).
  3. For a mirror image, the line \(l\) is the perpendicular bisector of the segment \(AB\).
    That means:
    \(l\) is perpendicular to \(AB\),
    and it cuts \(AB\) exactly in the middle.
  4. Take any point P on the line \(l\).
    A key mirror fact is: every point on the mirror is the same distance from a point and its image.
  5. So the distance from P to A equals the distance from P to B.
    Write this as:
    \(PA\) and \(PB\),
    \(PA = PB\).
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NCERT Exemplar Solutions Class 6 – Mathematics – Unit 9: Symmetry and Practical Geometry – Fill in the Blanks | Detailed Answers