# Computer Graphics - Graphics Operations

21:
Which of the following points lies on the same side as the origin, with reference to the line 3x + 7y = 2 ?
 A. (3,0) B. (1,0) C. (0.5,0.5) D. (0.5,0) Answer Report Discuss Option: D Explanation : If (0, 0) is substituted in the equation, we get 0, which is less than 2. So, any point on the same side as that of the origin, should yield a value less than 2, when substituted in the equation. Hence the result Click on Discuss to view users comments. Write your comments here:
22:
Which one of the following is not a linear transformation?
 A. F: R3 → R2 defined by f (x, y, z) = (x, z) B. F: R3 → R3 defined by f (x, y, z) = (x, y - 1, z) C. F: R2 → R2 defined by F (x,y) = (2 x, y -x) D. F: R2 → R2 defined by f (x,y) = (y, x) Answer Report Discuss Option: B Explanation : A function F(x , y ) x (a, b) is linear if F (ax, ay) = a F (x,y) and F (a+x, b+y) = F (a, b)+ F (x,y). The functions given in options (a), (c), (d) satisfy these two conditions but option (b) doesn't Click on Discuss to view users comments. Write your comments here:
23:

The entire graph of the function f(x) = x2 + kx - x + 9 is strictly above the x-axis if and only if

 A. - 3 < k < 5 B. - 3 < k < 2 C. - 3 < k < 7 D. - 5 < k < 7 Answer Report Discuss Option: D Explanation : y = x2 + (k- 1) x + 9 = (x + (k -1)/2)2 - ((k- 1)/2? + 9 For the entire graph to lie above the x-axis. y should be greater than 0, for all x. So, 9 - ((k- 1) / 2) 2  > 0  i.e., (k - 7) (k+ 5) < 0 or - 5 <  k < 7 Click on Discuss to view users comments. Write your comments here:
24:
Perform window to viewport transformation for the point (20, 15). Assume that (Xwmin, Ywmin) is (0, 0) (Xwmax, Ywmax) is (100, 100); (Xvmin, Yvmin) is (5, 5); (Xvmax ,Yvmax) is (20, 20).
The value of x and y in viewport is

 A. x=4,y=4 B. x=3,y=3 C. x=8,y=7.25 D. x=3,y=4 Answer Report Discuss Option: C Explanation : x(view port) = (XV max - XV min) (XW - XW min) / (XW max - XW min) + XVmin    y(viewport) = (YVmax - YVmin)( YW - YWmin) / (YWmax- YWmin ) + YVmin Click on Discuss to view users comments. Write your comments here:
25:
If (a, b, c) x (1, 3, 1) = (2, 1,6), where x denotes the vector product, then (a, b, c) is given by
 A. (0, 1, 1) B. (k, 0, 1 -k) for any real k C. (-1,2, -7) D. there exists no solution Answer Report Discuss Option: D Explanation :   The determinant given above  = (2,1,6) It gives the three equations, b - 3 c = 2; c - a = 1;  3a-b = 6. This system of equations, has no solution as using the second equation in the third gives b - 3c = -3, which contradicts the first. Click on Discuss to view users comments. Write your comments here: