In a CAD package, mirror image of a 2D point P (5, 10) is to be obtained about a line which passes through the origin and makes an angle of 45° counterclockwise with the X-axis. The coordinates of the transformed point will be
A)(7.5, 5)
B)(10, 5)
C)(7.5, -5)
D)(10, -5)

Question

Quizplus · Accepted Answer

The mirror image of a point P(x, y) about a line making an angle θ with the x-axis can be found using rotation and reflection transformations. First, rotate the point by -θ to align the mirror line with the x-axis, then reflect it over the x-axis, and finally rotate it back by θ. For a 45° angle, this simplifies to swapping the x and y coordinates of the point and then inverting the sign of the new y-coordinate to get the mirror image. Thus, the mirror image of (5, 10) about a line making a 45° angle with the x-axis is (10, -5), which is option D.

In a CAD Package, Mirror Image of a 2D Point