 Hello and welcome to the session. In this session we will discuss translation and dilation of geometric figures on a coordinate plane using matrices. First of all let us discuss vertex matrix. Now every point on a coordinate plane can be represented by matrices. The order x, y can be represented by a column matrix having elements x and y. Now suppose we have three points on a coordinate plane that is point A with coordinates 1, 2, point B with coordinates 3, 4 and point C with coordinates 2 minus 1. Now joining all these points we get a triangle that is triangle A, B, C. So points A, B and C from the vertices of a triangle. Now we can represent the triangle A, B, C with vertices A, B and will be the coordinates of that is 1 and 2. Then elements in second column will be the coordinates of point B that is 3 will be the coordinates of point C. Vertex matrix in row 1 in this matrix. Now we can write a vertex matrix. Now matrices can be used to perform transformations. Now translation means position without changing its shape and size that is sliding a figure. Now we write to translate a figure. Now suppose to translate the triangle in matrix in which the value to be added or in row 2. Now in the vertex matrix we have of this vertex matrix is now the dimension of the vertex matrix and translation matrix. So dimension of translation matrix will also be, now let us write the translation matrix. This is a matrix with elements in first row as minus 2, minus 2 and minus 2, 3, 3 and from x coordinate we have written 3 have to find coordinates of the translated image. So we will add vertex matrix and the translation the vertex matrix and the two matrices equal to matrix with elements in first row as 4 plus 3, minus 1 plus 3. This is equal to matrix with elements in first row as 1 minus 2 that is minus 1, then 1 and 0 and elements in resultant matrix will give us the coordinates of the translated image. The translated image will have vertices h with coordinates similarly b dash with coordinates 1 and 7 these points on the coordinate plane. So we have plotted these three points on the coordinate plane. Now joining these three points we get triangle a dash b dash c dash which is the translated image of triangle a b c. Then we added vertex matrix. Now let us discuss dilation. Now in dilation and we multiply the coordinates by a constant known as scale factor. Now in dilation using matrices we will use the multiple in dilating a pre-image using matrices. We write the vertex matrix pre-image which we multiply the matrix with the given scaling number also known as scalar in matrix. Now suppose we want to dilate that is triangle is twice that of the pre-image the image is twice the perimeter of pre-image then the length of the site of the figure will be twice the measure of the site of the original figure. Now this is the vertex matrix of triangle a b c. Now we multiply it by the scale factor 2. Now we want to multiply this vertex matrix by instead of vertex matrix by the scalar matrix with element 1 2 into 3 2 into 2 minus 1. Further this is equal to matrix with elements in first two vertices. Now let us plot these three points we get b dash c dash is the dilated image of triangle we have discussed with figures on a coordinate plane using matrices and this completes our session hope you all have enjoyed the session.