We will discuss here about reflection of a point in a line parallel to the xaxis.
Let P be a point whose coordinates are (x, y), AB be a line parallel the xaxis and the distance of AB from the xaxis 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 y + 2a while the xcoordinate will be the same as that of P.
The image of the point (x, y) in the line parallel to the xaxis at a distance form the xaxis (i.e., y = a) is the point(x, y + 2a), where a is taken positive if the line is on the positive side of the yaxis and a is taken negative if the line is on the negative side of the yaxis.
Examples:
(i) The image of the point (2, 4) in the line parallel to the xaxis at a distance 1 unit above the xaxis (i.e., y = 1) is (2, 4 + 2 × 1), i.e., (2, 2)
(ii) The image of the point (3, 5) in the line parallel to the xaxis at a distance 2 units below the xaxis (i.e., y = 2) is (3, 5 + 2 × (2)), i.e., (3, 9)
10th Grade Math
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