We will discuss here how to solve the problems on reflection in lines parallel to axes (x = a or y = b).
The coordinates of the points P and Q are (5, 4) and (2, 10) respectively.
(i) Find the point P’ and Q’onto which the points P and Q map on reflection in the line AB which is parallel to the xaxis and is at a distance 3 on the positive side of the yaxis.
(ii) Find the point P” and Q”onto which the points P and Q map on reflection in the line CD which is parallel to the yaxis and is at a distance 3 on the negative side of the xaxis.
Solution:
(i) We know that the image of the point (x, y) in the line parallel to the xaxis and at a distance a from the xaxis in the positive side of the yaxis is the point (x, y + 2a). Here, a = 3 and the coordinates of P are (5, 4). So, the coordinates of P’ are (5, (4) + 2 × 3), i.e., (5, 10). The coordinates of Q are (2, 10). So the coordinates of Q’ are (2, 10 + 2 × 3), i.e., (2, 4).
(ii) We know that the image of the point (x, y) in the line parallel to the yaxis and at a distance a from the yaxis in the negative side of the xaxis is the point (x + 2a, y). Here, the coordinates of P are (5, 4) and a = 3. So, the coordinates of P” are (5 + 2 (3), 4), i.e., (11, 4). The coordinates of Q are (2, 10). So the coordinates of Q” are (2 + 2(3), 10), i.e., (4, 10).
10th Grade Math
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