# Reflection of a Point in x-axis

How to find the co-ordinates of the reflection of a point in x-axis?

To find the co-ordinates in the adjoining figure, x-axis represents the plain mirror. M is the point in the rectangular axes in the first quadrant whose co-ordinates are (h, k).

When point M is reflected in x-axis, the image M’ is formed in the fourth quadrant whose co-ordinates are (h, -k). Thus we conclude that when a point is reflected in x-axis, then the x-co-ordinate remains same, but the y-co-ordinate becomes negative.

Thus, the image of point M (h, k) is M' (h, -k).

Rules to find the reflection of a point in the x-axis:

(i) Retain the abscissa i.e., x-coordinate.

(ii) Change the sign of ordinate i.e., y-coordinate.

Examples to find the co-ordinates of the reflection of a point in x-axis:

1. Write the co-ordinates of the image of the following points when reflected in x-axis.

(i) (-5 , 2)

(ii) (3, -7)

(iii) (2, 3)

(iv) (-5, -4)

Solution:

(i)The image of (-5 , 2) is (-5 , -2).

(ii) The image of (3, -7) is (3, 7).

(iii) The image of (2, 3) is (2, -3).

(iv) The image of (-5, -4) is (-5, 4).

2. Find the reflection of the following in x-axis:

(i) P (-6, -9)

(ii) Q (5, 7)

(iii) R (-2, 4)

(iv) S (3, -3)

Solution:

The image of P (-6, -9) is P' (-6, 9).

The image of Q (5, 7) is Q' (5, -7) .

The image of R (-2, 4) is R' (-2, -4) .

The image of S (3, -3) is S' (3, 3) .

Solved example to find the reflection of a triangle in x-axis:

3. Draw the image of the triangle PQR in x-axis. The co-ordinate of P, Q and R being P (2, -5); Q (6, -1); R (-4, -3)

Solution:

Plot the points P (2, -5); Q (6, -1); R (-4, -3) on the graph paper. Now join PQ, QR and RP; to get a triangle PQR.

When reflected in x-axis, we get P' (2, 5); Q' (6, 1); R' (-4, 3). Now join P'Q', Q'R' and R'P'.

Thus, we get a triangle P'Q'R' as the image of the triangle PQR in x-axis.

Solved example to find the reflection of a line-segment in x-axis:

4. Draw the image of the line segment PQ having its vertices P (-3, 2), Q (2, 7) in x-axis.

Solution:

Plot the point at P (-3, 2) and at Q (2, 7) on the graph paper. Now join P and Q to get the line segment PQ.

When reflected in x-axis P (-3, 2) become P' (-3, -2) and Q (2, 7) become Q' (2, -7) on the same graph. Now join P'Q'.

Therefore, P'Q' is the image of PQ when reflected in x-axis.

Note: Point M (h, k) has image M' (h, -k) when reflected in x-axis.

Thus, we conclude that when the reflection of a point in x-axis:

• x-axis acts as a plane mirror.
• M is the point whose co-ordinates are (h, k).
• The image of M i.e. M' lies in fourth quadrant.
• The co-ordinates  of M' are (h, -k).

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