How to find the coordinates of the reflection of a point in xaxis?
To find the coordinates in the adjoining figure, xaxis represents the plain mirror. M is the point in the rectangular axes in the first quadrant whose coordinates are (h, k).
When point M is reflected in xaxis, the image M’ is formed in the fourth quadrant whose coordinates are (h, k). Thus we conclude that when a point is reflected in xaxis, then the xcoordinate remains same, but the ycoordinate becomes negative.
Thus, the image of point M (h, k) is M' (h, k).
Rules to find the reflection of a point in the xaxis:
(i) Retain the abscissa i.e., xcoordinate.
(ii) Change the sign of ordinate i.e., ycoordinate.
Examples to find the coordinates of the reflection of a point in xaxis:
1. Write the coordinates of the image of the following points when reflected in xaxis.
(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 xaxis:
(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 xaxis:
3. Draw the image of the triangle PQR in xaxis. The coordinate 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 xaxis, 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 xaxis.
Solved example to find the reflection of a linesegment in xaxis:
4. Draw the image of the line segment PQ having its vertices P (3, 2), Q (2, 7) in xaxis.
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 xaxis 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 xaxis.
Note: Point M (h, k) has image M' (h, k) when reflected in xaxis.
Thus, we conclude that when the reflection of a point in xaxis:
● Related Concepts
● Order of Rotational Symmetry
● Reflection of a Point in yaxis
● Reflection of a point in origin
● Rotation
● 90 Degree Clockwise Rotation
● 90 Degree Anticlockwise Rotation
7th Grade Math Problems
8th Grade Math Practice
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