1. Find the image of the given point under the transformation with the given matrix.

Ans: (14, 14)

3.Find the image of the given point under the transformation with the given matrix

Ans:(-18, -1)

5. Find the images of (3,4) and (2,7) under a scale change of 3 units in the x direction.

Ans: (9,4), (6,7).

7. Find the images of (4,1) and (-2,3) under a reflection about the line y = x.

Ans: (1,4), (3, -2).

9. Find the images of (0,3), (7,0) and (5,5) under a reflection about the x-axis.

Ans: (0,3), (7,0), (5,-5).

11. Find the images of (2,2), (3,3), (4,4) and (5,5) under a rotation of 180º.

Ans: (-2,-2), (-3,-3), (-4, -4), (-5,-5).

13. Find the images of (-5,4), (-2,-3), (-5,-2), (-1,3) and (-6,5) under a scale change of 5 units in both the x and y directions.

Ans: (-25,20), (-10, -15), (-25, -10), (-5, 15), (-30, 25).

15. Sketch a triangle with vertices (6,5), (7,3) and (8,2) and its image under a shear with the given matrix on the same set of axes.

Solution:

17. Sketch a quadrilateral with vertices (3,3), (9,3), (9,5) and (3,5) and its image under a rotation of 90º on the same set of axes..

Solution:

19. Sketch a hexagon with vertices (3,2), (7,3), (8,7), (6,10), (2,6), and (-2,4) and its image under a rotation of 270º on the same set of axes..

Solution:

21. Find the matrix representing the product of a rotation of 270º followed by a reflection about the x-axis.

Solution:

23. Find the image of the triangle (3,9), (5,2) and (7,4) under a reflection about the x-axis followed by a rotation of 270º.

Solution: (-9, -3), (-2, -5), (-4,-7).

25. For which of the special 2x2 matrices listed in this section is the concept of the slope of a segment generally (except possibly for some special cases) an invariant property?.

Solution: Identity, scaling change in both x and y directions.

26. Show that a translation cannot be done by multiplication by a 2x2 matrix.

Solution: The image of the point (0,0) under any 2x2 matrix is (0,0), hence, this point cannot be translated by such a multiplication.