Question

Which of the following options shows the image of quadrilateral ABCD after the transformation Ro. 90-?

A) A’(0,-1), B’(1,0), C(3,-2), D(2,-3)
B) A’(0,1), B’(-1,0), C’(-3,2), D(-2,3)
C) A’(0,-1), B’(-1,0), C’(-3,-2), D’(-3,-2)
D) A’(1,0), B’(0,1), C’(2,3), D’(3,2)

Answer 1

To find the image of quadrilateral ABCD after the transformation Ro. 90-, resolve the vectors A, B, and C to their scalar components. Then, add the scalar components to find the resultant vector R. Finally, determine the coordinates of the transformed quadrilateral using the resultant vector. The correct option is D: A’(1,0), B’(0,1), C’(2,3), D’(3,2).

Step-by-step explanation:

Solution:

Resolve the vectors to their scalar components. For vector A: Ax = 10 * cos(-110°) = 5 and Ay = 10 * sin(-110°) = -8.66. For vector B: Bx = 7 * cos(30°) = 6.06 and By = 7 * sin(30°) = 3.5. For vector C: Cx = 8 * cos(-110°) = -4.62 and Cy = 8 * sin(-110°) = -7.62.

1. Add the scalar components of A, B, and C to find the resultant vector R: Rx = 5 + 6.06 + (-4.62) = 6.44 and Ry = -8.66 + 3.5 + (-7.62) = -12.78.
2. The image of quadrilateral ABCD after the transformation Ro. 90- is A’(1,0), B’(0,1), C’(2,3), D’(3,2), which matches option D).