We will discuss here about reflection of a point in a line parallel to the yaxis.
Let P be a point whose coordinates are (x, y), AB be a line parallel the xaxis and the distance of AB from the yaxis be a. Let the image of P be P’ in the line AB
Clearly, P’ will be similarly situated on that side of AB which is opposite to P. So, the ycoordinates of P’ will be –x + 2a while the ycoordinate will be the same as that of P.
The image of the point (x, y) in the line parallel to the yaxis at a distance from the yaxis (i.e., x = a) is the point (x + 2a, y), where a is taken positive if the line is on the positive side of the xaxis and a is taken negative if the line is on the negative side of the xaxis.
Examples:
(i) The image of the point (2, 4) in the line parallel to the yaxis at a distance 1 unit above the yaxis (i.e., x = 1) is (2 + 2 × 1, 4), i.e., (0, 4)
(ii) The image of the point (3, 5) in the line parallel to the yaxis at a distance 2 units below the xaxis (i.e., x = 2) is (3 + 2 × (2), 5), i.e., (1, 5)
10th Grade Math
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