 Hello and welcome to the session. In this session we discussed the following question which says the triangle A, B, C where A has coordinates 1, 2, B has coordinates 4, 8 and C has coordinates 4, 1 is reflected in the line y equal to 0 onto the triangle A dash B dash C dash and then triangle A dash B dash C dash is reflected in the origin onto the triangle A double dash B double dash C double dash write down the coordinates of first A dash B dash and C dash and A double dash B double dash and C double dash. First of all we discussed the reflection in the x-axis and reflection in the origin Rx which goes from xy to x minus y. This represents reflection in the x-axis that is reflection in the x-axis maps the point with coordinates x and y onto the point with coordinates x minus y that is the sign of the ordinate is changed. Then next we have RO goes from xy to minus x minus y. This represents the reflection in the origin. Reflection in the origin maps the point with coordinates x and y onto the point with coordinates minus x minus y that is signs of both the abscissa and the ordinate changes under the reflection in the origin. This is the key idea that we use for this question. Let's proceed with the solution now. In the question we are given that the triangle abc where the coordinates of the points ab and c are given to us is reflected in the line y equal to 0 onto the triangle A dash B dash C dash. Now first of all we say that the line y equal to 0 means the x-axis so this means the triangle abc is reflected in the x-axis onto the triangle A dash B dash C dash and we are supposed to write down the coordinates of A dash B dash and C dash. We have the coordinate of the point A 1 2 point B has coordinates 4 8 and point C has coordinates 4 1. Now triangle abc is reflected in the x-axis onto the triangle A dash B dash C dash and we know that reflection in the x-axis is denoted by this so this means to find the coordinates of the points A dash B dash and C dash we need to change the sign of the y coordinates of the points AB and C respectively so the coordinates of the point A dash is 1 minus 2 that is the x coordinate remains as it is and the sign of the y coordinate changes then coordinates of the point B dash is given by changing the sign of the y coordinate that is it becomes 4 minus 8 and coordinates of the point C dash is given by changing the sign of the y coordinate that is it becomes 4 minus 1. So in the first part we were supposed to write down the coordinates of A dash B dash and C dash. Now next we have that the triangle A dash B dash C dash is reflected in origin onto the triangle A double dash B double dash C double dash that is triangle A dash B dash C dash is reflected in the origin onto the triangle A double dash B double dash C double dash and we are supposed to write down the coordinates of A double dash B double dash and C double dash now we know that the reflection in the origin is represented by this so this means to write down the coordinates of the point A double dash B double dash and C double dash we need to change the signs of both the abscissa and the ordinate of the points A dash B dash and C dash respectively so now coordinates of the point A double dash is given by changing the sign of the abscissa and the ordinate of the point A dash so it would be minus 1 and 2 in the same way to write down the coordinates of the point B double dash we need to change the sign of both the abscissa and the ordinate of the point B dash and so its coordinates is given by minus 4 8 then coordinates of the point C double dash is given by changing the sign of both the abscissa and the ordinate of the point C dash and so its coordinates are given by minus 4 1 so here we have got the coordinates of the points A double dash B double dash and C double dash so we have got the answer for both the parts of the question this completes the session hope you have understood the solution of this question