How to find the coordinates of the reflection of a point in origin?
To find the coordinates in the adjoining figure, origin represents the plane mirror. M is the any point in the first whose coordinates are (h, k). When point M is reflected in the origin, the image M’ is formed in the third quadrant whose coordinates are (h, k).
Thus, we conclude that when a point is reflected in origin, both xcordinate and ycoordinate 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., xcoordinate.
(ii) Change the sign of ordinate i.e., ycoordinate.
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).
Workedout examples to find the coordinates 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 coordinates are (h, k).
The image of M, i.e., M’ lies in the third quadrant and the coordinates of M’ are (h, k).
`● Related Concepts
● Order of Rotational Symmetry
● Reflection of a Point in xaxis
● Reflection of a Point in yaxis
● Rotation
● 90 Degree Clockwise Rotation
● 90 Degree Anticlockwise Rotation
7th Grade Math Problems
8th Grade Math Practice
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