 Hello and welcome to the session. In this session we will discuss a question which says that a square a v c d has vertices a with coordinates minus 1 3 b with coordinates 3 3 c with coordinates 3 minus 1 and d with coordinates minus 1 minus 1. Find the image of the square after reflection in y-axis. Now before starting the solution of this question we should know a result and that is reflection in y-axis. Now to reflect any figure in y-axis on the coordinate plane we multiply the vertex matrix on the left by the 2 cross 2 matrix that is the matrix with elements in first row as minus 1 0 and elements in second row as 0 1. Now this result will work out as a key idea for solving out the given question. Now let us start with the solution of the given question. Now we have given square a v c d on the coordinate plane. Now vertices are given to us as a v c and the coordinates of all these vertices are also given. So let us draw these points on the coordinate plane. So we have plotted to these points we get the square a v c d. First of all we write the vertex of row 1 is a matrix with elements minus 1 minus 1 with the coordinates of the reflected. Now from the key idea we know that as minus 1 0 0 1. Now let us find the product of this vertex matrix. Now this is up to now here number of columns of this square matrix is equal to number of rows of this vertex matrix. So this product is defined and the resulting matrix will be up to 2 cross 4. Now for obtaining the elements of the product of this first matrix by the corresponding that is the vertex matrix into minus 1 plus 0 into 3 when minus 1 into 3 plus 0 into 3 then we have minus 1 into 3 plus 0 into minus 1 into minus 1 plus 0 into minus 1 0 into minus 1 plus 1 into 3 then 0 into 3 plus 1 into 3 then 0 into 3 plus 1 into minus 1 0 into minus 1 plus 1 into minus 1 a matrix plus 0 minus 3 plus 0 minus 3 plus 0 and 1 plus 0 0 plus 3 0 plus 3 0 minus 1 and 0 minus 1. This is equal to matrix with elements in first row as 1 minus 3 and 1 3 3 minus 1 and minus 1. Now this product matrix will give us the vertices of the reflected image in y axis. This is the reflected image 1 3 b dash with coordinate minus 1 and d dash with coordinates 1 and minus 1. Now let us plot these points. So we have the image coordinates 1 3 b dash with coordinates minus 3 3 c dash with coordinates 1 minus 1 b dash c dash d dash of square a b c d in variation of the given question and that's all for the session. Hope you all have enjoyed the session.