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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