Question

Triangle ABC is rotated 180º using the origin as the center of rotation.

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

Which sequence of transformations will produce the same result?
a translation up 4 and then a reflection over the y-axis
a translation up 4 and then a translation right 6
a reflection over the x-axis and then a reflection over the y-axis
a translation right 6 and then a reflection over the x-axis
Mark this and return

Answer 1

a reflection over the x-axis and then a reflection over the y-axis

Reason: reflecting (x,y) over the x-axis gives (x,-y), then over the y-axis gives (-x,-y), which is the same as a 180° rotation about the origin. For example, (-4,-3) -> (-4,3) -> (4,3).