Question

From the figure, find the coordinates of A,B,C,D,E and F. Which are the points are mirror images in (i) x-axis, (ii) y-axis.

Answer 1

Hint: In this question it is given that from the figure we have to find the coordinates of the points A,B,C,D,E and F, and after that we have to find which points are mirror images w.r.t x-axis and y-axis. So to find their coordinates we have to measure the distance from the origin to the point along x-axis and then along y-axis, if the distance of any point along x-axis be a and along y-axis be b then the coordinate of the point will be (a,b) and the mirror image of that point (a,b) w.r.t x-axis is (a,-b) and w.r.t y-axis becomes (-a,b).
Complete step by step answer:
First of all we are going to find the coordinate of the point C.

So from the above we can observe that, from the origin the distance of point C along x-axis is 5unit and along y-axis distance is again 5 unit, so the coordinate of point C is (5,5).

Similarly we can say that the coordinate of point A,B,D,E and F is (2,2),(1,4),(0,4),(2,-2) and (-5,-5) respectively.

Now we have to find the points which are the mirror image of each other, so as we mentioned earlier that the mirror image of any point (a,b) w.r.t x-axis is (a,-b) and w.r.t y-axis becomes (-a,b).
So from the above we can say that the point E(2,-2) is the mirror image of A(2,2) and x-axis is the mirror in this case, and D(0,4) is the mirror image of itself and the mirror is y-axis because we can write (0,4) as (-0,4) so by this we can say that in this case the point itself is a mirror image.
Note: While finding the mirror image of any point you have to keep in mind that the mirror image always forms with respect to x-axis or y-axis, and if it is respect to x-axis then the distance of that reflected point from the x axis is equal to the distance of the original point but their position will be vertically opposite, i.e, lies on two different side of x axis, similarly this will apply for y-axis also.