Reflection of a Point in a Line Parallel to the x-axis

We will discuss here about reflection of a point in a line parallel to the x-axis.

Let P be a point whose coordinates are (x, y), AB be a line parallel the x-axis and the distance of AB from the x-axis 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 y-coordinates of P’ will be -y + 2a while the x-coordinate will be the same as that of P.

The image of the point (x, y) in the line parallel to the x-axis at a distance form the x-axis (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 y-axis and a is taken negative if the line is on the negative side of the y-axis.


Examples:

(i) The image of the point (2, 4) in the line parallel to the x-axis at a distance 1 unit above the x-axis (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 x-axis at a distance 2 units below the x-axis (i.e., y = -2) is (-3, -5 + 2 × (-2)), i.e., (-3, -9)






10th Grade Math

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