Question

ΔABC underwent a sequence of rigid transformations to give ΔA′B′C′. Which transformations might have taken place?

a reflection across the y-axis followed by a reflection across the x-axis

a rotation 90° clockwise about the origin followed by a reflection across the x-axis

a rotation 270° clockwise about the origin followed by a reflection across the x-axis

a reflection across the x-axis followed by a reflection across the y-axis

Answer 1

"A rotation 90° clockwise about the origin followed by a reflection across the x-axis" is the one among the following choices given in the question that describes which transformations might have taken place. The correct option among all the options that are given in the question is the second option. I hope the answer has helped you.

Answer 2

Answer: The correct option is second, a rotation $90^{\circ}$ clockwise about the origin followed by a reflection across the x-axis.

Explanation:

From the given figure it is noticed that the vertices of ΔABC are A(-6,4), B(-4,6), C(-2,2) and vertices of ΔA'B'C' are A'(4,-6), B(6,-4), C(2,-2).

It means if the point is P(x,y) then after transformation it will be P'(y,x).

If a point P(x,y) reflection across the y-axis followed by a reflection across the x-axis, then the image of point after transformation will be P'(-x,-y), therefore it is not the correct option.

If a shape is rotated $90^{\circ}$ clockwise about the origin then the  point P(x,y) will be P'(y,-x) and after that reflect across the x-axis, so the point after transformation will be P'(y,x), therefore it is the correct option.

If a shape is rotated $270^{\circ}$ clockwise about the origin then the  point P(x,y) will be P'(-y,x) and after that reflect across the x-axis, so the point after transformation will be P'(-y,-x), therefore it is not the correct option.

If a point P(x,y) reflection across the x-axis followed by a reflection across the y-axis, then the image of point after transformation will be P'(-x,-y), therefore it is not the correct option.

Hence, the correct option is second, a rotation $90^{\circ}$ clockwise about the origin followed by a reflection across the x-axis.