Question

Mrs. Hamilton shows her students this graph and asks them to determine how figure A was transformed to figure B.

On a coordinate plane, triangle A has points (negative 1, 0), (negative 2, 4), (negative 1, 4). Triangle B has points (3, 1), (3, 5), (4, 5)..

Marcus suggests that figure A was reflected over the y-axis and then translated 2 to the right and 1 up. Julianne agrees, and states that the transformations could happen in any order. Which best describes the accuracy of Julianne’s statement?
Accurate. A translation of figure A of 2 to the right and 1 up and then a reflection over the y-axis produces the image, figure B.
Accurate. A reflection over the y-axis and then a translation of 1 up and 2 to the right produces the image, figure B.
Inaccurate. A translation of 2 to the right and 1 up and then a reflection over the y-axis results in a figure that is located in the second quadrant.
Inaccurate. A reflection over the y-axis and then a translation of 1 up and 2 to the right results in a figure that is located in the second quadrant.

Answer 1

Inaccurate. If you reflect A over the y-axis you get (1,0), (2,4), (1,4), and then translating 2 right and 1 up gives (3,1), (4,5), (3,5) = B. But if you translate A first by (2,1) you get (1,1), (0,5), (1,5), and then reflecting gives (-1,1), (0,5), (-1,5), which lies in the second quadrant. So the order matters — choose option 3.