Question

Triangle ABC has coordinates: A(1,2), B(3,5), and C(5,1). You rotate triangle ABC about (1,1) 180° clockwise and then translate the triangle A’B’C’ by vector. Then you reflect A"B"C" across y=x. Where is A"’?

a) (-1, 1)
b) (1, -3)
c) (3, -1)
d) (5, -5)

Answer 1

The question is incomplete without the specific translation vector; therefore, it's not possible to accurately determine the final coordinates of A"'. This confusion might arise due to an oversight in the question or a misprint.

Step-by-step explanation:

Given the problem where Triangle ABC has coordinates: A(1,2), B(3,5), and C(5,1). The task involves rotating it 180° about the point (1,1), translating it by a vector (not specified in the question), and then reflecting it across the line y=x. To solve this, we go step by step. A 180° rotation around (1,1) will reflect a point across this center. Therefore, the rotation takes point A to A', B to B', and C to C'. For A, the transformation is (1-(1-1), 1-(2-1)) = (1, 0). Then, A' is translated by a vector (also not specified in the question), giving us A". Finally, A" is reflected across y=x to get A"'. When reflecting a point across y=x, the x- and y-coordinates exchange places. If A" were a point with coordinates (x,y), A"' would be (y, x). Without the translation vector details, we cannot provide A"', however, if the vector was (0,0), A"' would be (0,1), which is not one of the options given. Hence, the correct answer is not determinable without the translation vector.