![]() Subtracting (ii) from (i) we get, -2y' = 2x or y' = -x (ii)Īdding (i) and (ii) we get, 2y = - 2x' or x' = -y Then, slope of the line segment PP', m 2 = \(\frac 2\)) Let (x', y') be the co- ordinates of the point P'. ![]() Then P' is the image of the point P under reflection about the line y = x. Draw perpendicular PM from the point P to the line y = x and produce it to the point P' such that PM = MP'. Then, slope of the line, m 1 = tan 45° = 1. Y = x is the equation of the line which makes an angle of 45° with the positive direction of X- axis. Hence, if R denotes the reflection in the line x = k, then: ∴ Image of point P (x, y) after reflection in the line x = k is P' (2k - x, y). ∴ Co- ordinates of the point P' are (2k - x, y). ![]() Since, M is the mid- point of the line segment PP', then by mid- point formula, Then P' is the image of P after reflection in the line x = k. Draw a perpendicular PM from P to the line x = k and produce it to the point P' such that PM = MP'. So, the reflection in a line parallel to Y- axis means reflection in the line x = k. The equation of a line parallel to Y- axis is given by x = k where k is X - intercept of the line.
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