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