How to find the co-ordinates of the reflection of a point in origin?
To find the co-ordinates in the adjoining figure, origin represents the plane mirror. M is the any point in the first whose co-ordinates are (h, k). When point M is reflected in the origin, the image M’ is formed in the third quadrant whose co-ordinates are (-h, -k).
Thus, we conclude that when a point is reflected in origin, both x-c-ordinate and y-co-ordinate become negative. Thus, the image of M (h, k) is M’ (-h, -k).
Rules to find the reflection of a point in the origin:
(i) Change the sign of abscissa i.e., x-coordinate.
(ii) Change the sign of ordinate i.e., y-coordinate.
For example:
1. The reflection of the point A (5, 7) in the origin is the point A' (-5, -7).
2. The reflection of the point B (-5, 7) in the origin is the point B' (5, -7).
3. The reflection of the point C (-5, -7) in the origin is the point C' (5, 7).
4. The reflection of the point D (5, -7) in the origin is the point D' (-5, 7).
5. The reflection of the point E (5, 0) in the origin is the point E' (-5, 0).
6. The reflection of the point F (0, 7) in the origin is the point F' (0, -7).
7. The reflection of the point G (-5, 0) in the origin is the point G' (5, 0).
8. The reflection of the point H (0, -7) in the origin is the point H' (0, 7).
Worked-out examples to find the co-ordinates of the reflection of a point in origin:
1. What is the reflection of the following in origin?
(i) P (1, 4)
(ii) Q (-3, -7)
(iii) R (-5, 8)
(iv) S (6, -2)
Solution:
(i) The image of P (1, 4) is P’ (-1, -4).
(ii) The image of Q (-3, -7) is Q’ (3, 7).
(iii) The image of R (-5, 8) is R’ (5, -8).
(iv) The image of S (6, -2) is S’ (-6, 2).
Note:
Thus, we conclude that the origin acts as a plane mirror. M is the point whose co-ordinates are (h, k).
The image of M, i.e., M’ lies in the third quadrant and the co-ordinates of M’ are (h, -k).
● Related Concepts
● Order of Rotational Symmetry
● Reflection of a Point in x-axis
● Reflection of a Point in y-axis
● Rotation
● 90 Degree Clockwise Rotation
● 90 Degree Anticlockwise Rotation
7th Grade Math Problems
8th Grade Math Practice
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