 Hello and welcome to the session. In this session we are going to discuss the following question and the question says that Find the new coordinates of the points minus 4 minus 1 and 3 minus 3 When the axis are translated to the new origin with coordinates 1, 4 Before starting the solution of this question we should know our result. If the coordinates of the origin O' of the translated system are HK related to the original system then the new and the old coordinates are related using the following result and that is X is equal to X' plus H or X' is equal to X minus H and Y is equal to Y' plus K or Y' is equal to Y minus K So the coordinates of the point P in the new axis are given by X minus H, Y minus K Similarly original coordinates of point P are given by X' plus H, Y' plus K With this key idea we shall proceed to the solution In this question we are given two points having coordinates minus 4 minus 1 and 3 minus 3 In the original coordinate axis we have to find new coordinates for these points when the axes are translated to the new origin having coordinates 1, 4 So we are given two points with coordinates minus 4 minus 1 and 3 minus 3 In the original coordinate axis and coordinates of new origin are given by 1, 4 So here the ordered pair HK is given by the ordered pair 1, 4 which implies H is equal to 1 and K is equal to 4 Now using the key idea we know that new and the old coordinates are related by the following result So the coordinates of point P in new axis are given by X minus H, Y minus K So here new coordinates that is X', Y' will be given by the ordered pair X minus H, Y minus K as H is equal to 1 and K is equal to 4 So the coordinates X', Y' will be equal to the ordered pair X minus 1, Y minus 4 And here we have the first point as the ordered pair minus 4, minus 1 So new point in the new axis will be the ordered pair X minus 1, Y minus 4 that is minus 4, minus 1, minus 1, minus 4 which is equal to the ordered pair minus 5, minus 5 And the second point is given by the ordered pair 3 minus 3 So new point in the new axis will be given by the ordered pair X minus 1, Y minus 4 and this is equal to the ordered pair 3 minus 1, minus 3, minus 4 and this is equal to the ordered pair 2 minus 7 Now let us see these points in the translated axis The origin O with coordinates 00 is translated to the new origin O' with coordinates 14 by moving 1 unit right and 4 units up and new axes are drawn at this point Now we can see that the points with coordinates 3 minus 3 and minus 4 minus 1 have been plotted according to the original axis Now we see the point with coordinates 3 minus 3 with respect to the new origin that is O' Now we see that to reach the point with coordinates 3 minus 3 from new origin O' we will have to move 2 units right and 1, 2, 3, 4, 5, 6, 7 that is 7 units down from origin O' So the new coordinates are given by 2 minus 7 Similarly to reach the point with coordinates minus 4 minus 1 from O' we have to move 1, 2, 3, 4, 5 that is 5 units left and 1, 2, 3, 4, 5 5 units down from new origin O' So its new coordinates will be minus 5 minus 5 with respect to the new axes Therefore the new coordinates of the points minus 4 minus 1 and 3 minus 3 will be minus 5 minus 5 and 2 minus 7 respectively with respect to the new axes This completes our session Hope you enjoyed this session