We will discuss here about reflection of a point in the y-axis.
Reflection in the line x = 0 i.e., in the y-axis.
The line x = 0 means the y-axis.
Let P be a point whose coordinates are (x, y).
Let the image of P be P’ in the y-axis.
Clearly, P’ will be similarly situated on that side of OY which is opposite to P. So, the x-coordinates of P’ will be – x while its y-coordinates will remain same as that of P.
The image of the point (x, y) in the y-axis is the point (-x, y).
Symbolically, My (x, y) = (-x, y)
Rules to find the reflection of a point in y-axis:
(i) Change the sign of abscissa i.e. x-coordinate.
(ii) Retain the ordinate i.e., y-coordinate.
Therefore, when a point is reflected in the y-axis, the sign of its abscissa changes.
Examples:
(i) The image of the point (3, 4) in the y-axis is the point (-3, 4).
(ii)
The image of the point (-3, -4) in the y-axis is the point (-(-3), -4) i.e., (3,
-4).
(iii) The image of the point (0, 7) in the y-axis is the point (0, 7).
(iv) The image of the point (-6, 5) in the y-axis is the point (-(-6), 5) i.e., (6, 5).
(v) The reflection of the point (5, 0) in the y-axis = (-5, 0) i.e., My (5, 0) = (-5, 0)
Solved example to find the reflection of a point in the y-axis:
Find the points onto which the points (11, -8), (-6, -2) and (0, 4) are mapped when reflected in the y-axis.
Solution:
We know that a point (x, y) maps onto (-x, y) when reflected in the y-axis. So, (11, -8) maps onto (-11, -8); (-6, -2) maps onto (6, -2) and (0, 4) maps onto (0, 4).
● Reflection
10th Grade Math
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