Question

Select the final image of AABC after the given sequences of transformations. Translate AABC by (4,4),

rotate 90° counterclockwise around A, and reflect over the y-axis.

Answer 1

Explanation:

given A(-1, 2), B(-3, 4), C(-2, 5)

after translating by (4, 4)

points are A(-1 + 4, 2 + 4), B(-3 + 4, 4 + 4), C(-2 + 4, 5 + 4)

A(3, 6), B(1, 8), C(2, 9)

to rotate 90° counter clockwise (x, y) ----> (-y, x)

now it is rotated around point A(3, 6).That means A remains same and we need to find new coordinates of B and C. To find B and C let us make origin as A and find B ,C coordinates from it.

B'(1 - 3, 8 - 6) = (-2, 2)

C'(2 - 3, 9 - 6) = (-1, 3)

now it becomes (-y, x)

B'(-2, -2)

C'(-3, -1)

now we have to move origin from (3,6) to (0,0) again.

so B'(-2 + 3, -2 + 6) = (1, 4)

C'(-3 + 3 , -1 + 6) = (0, 5)

now reflection over y axis means (x, y) --> (-x, y)

A'(-3, 6)

B'(-1, 4)

C'(0, 5)

it is different from the options

but this is the process, tell me if you find any step different from the question

see the figure below