We will discuss here about reflection of a point in the x-axis.
Reflection in the line y = 0 i.e., in the x-axis.
The line y = 0 means the x-axis.
Let P be a point whose coordinates are (x, y).
Let the image of P be P’ in the axis.
Clearly, P’ will be similarly situated on that side of OX which is opposite to P. So, the y-coordinates of P’ will be – y while its x-coordinates will remain same as that of P.
The image of the point (x, y) in the x-axis is the point (x, -y).
Symbolically, M\(_{x}\) (x, y) = (x, -y)
Rules to find the reflection of a point in x-axis:
(i) Retain the abscissa i.e. x-coordinate.
(ii) Change the sign of ordinate i.e., y-coordinate.
Therefore, when a point is reflected in the x-axis, the sign of its ordinate changes.
Examples:
(i) The image of the point (3, 4) in the x-axis is the point (3, -4).
(ii) The image of the point (-3, -4) in the x-axis is the point (-3, -(-4)) i.e., (-3, 4).
(iii) The reflection of the point (5, -7) in the x-axis = (5, 7) i.e., M\(_{x}\) (5, -7) = (5, 7)
(iv) The reflection of the point (9, 0) in the x-axis is the point itself, therefore, the point (9, 0) is invariant with respect to x-axis.
(v) The reflection of the point (-a, -b) in the x-axis = (-a, b) i.e., M\(_{x}\) (-a, -b) = (-a, b)
Solved examples to find the reflection of a point in the x-axis:
1. Find the points onto which the points (11, -8), (-6, -2) and (0, 4) are mapped when reflected in the x-axis.
Solution:
We know that a point (x, y) maps onto (x, -y) when reflected in the x-axis. So, (11, -8) maps onto (11, 8); (-6, -2) maps onto (-6, 2) and (0, 4) maps onto (0, -4).
2. Which of the following points (-2, 0), (0, -5), (3, -3) are invariant points when reflected in the x-axis?
Solution:
We know that only those points which lie on the line are invariant points when reflected in the line. So, only those points are invariant which lie on the x-axis. Hence, the invariant points must have y-coordinate = 0.
Therefore, only (-2, 0) is the invariant point.
3. Which of the following points (7, 0), (-1, 1), (2, 2), (0, 4) are invariant points when reflected in the y-axis?
Solution:
We know that only those points which lie on the line are invariant points when reflected in the line. So, only those points are invariant which lie on the y-axis. Hence, the invariant points must have x-coordinate = 0.
Therefore, only (0, 4) is the invariant point.
● Reflection
10th Grade Math
From Reflection of a Point in the x-axis to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Feb 23, 24 03:55 PM
Feb 23, 24 02:24 PM
Feb 23, 24 01:28 PM
Feb 22, 24 04:15 PM
Feb 22, 24 02:30 PM
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.