The single transformation T is represented by the matrix 1 0

The single transformation T is represented by the matrix (1 0 0 -1). Give a geometrical description of the transformation. Calculate the coordinates of the image of the points A (2, 5) and B(-l, 3) under transformation T By finding the inverse of the matrix. Find the coordinates of the points of which (-5, -10) is the image. The transformation R is a rotation of 180 degree about the origin. Write down the matrix representing R. The transformation E is an enlargement of scale factor 2, center the origin. Write the matrix representing E. Determine the matrix C which represents the rotation R followed by the enlargement E. The graph below shows the line segment AC and its image A\'C\' after a transformation by the matrix (p r Q S) Write in the form of a single 2 times 2 matrix, the coordinates of A and C A\' and C\' Using matrices only. Write an equation to represent the transformation of AC onto A\'C\' Hence, use inverse matrix to determine the values of p, q, r and s.

Solution

1. a. The given matrix represents reflection in the x axis

2. Points are A(2,5) , B(-1,3)

On reflecting across x axis, x coordinate remains same and y coordinate changes

Therefore A\'(2,-5) And B\'(-1,-3)

C.Inverse matrix is

1 0

0 -1

Point is (-5,-10)

Coordinnate of the required point is (-5,10)