Question

The mirror image of point $M$$(h,k)$ taken about the origin is point $M$'. Find the quadrant which $M$' lies in.

Answer 1

The point $M$ is in the I quadrant when taking its mirror image about the origin, the point $M^{\prime }$ will be formed in the III quadrant. The point $M$ is $h$ units right of the origin and $k$ units above of origin. Similarly the image of the point $M$ i.e. $M^{\prime }$ will be $h$ units left of origin and $k$ units below of origin. Therefore the coordinates of point $M$' is $(-h,-k)$.

Since, the sign of abscissa and ordinate of point $M$' $(-h,-k)$ is negative.
Therefore, the point $M^{\prime }$ lies in ||| quadrant.