Anonymous
anonymous 3 years ago
if triangle abc is rotated 180 degrees, reflected over the y-axis, and reflected over the x-axis, where will point a' lie? (5, −4) (4, −5) (−4, 5) (−5, 4)
geometry

Given that triangle ABC with vertices at A(-5, 4), B(-7, 2) and C(-2, 3) is rotated 180 degrees, reflected over the y-axis, and reflected over the x-axis.

Assuming that the rotation of 180 degrees was about the origin, rotation of 180 degrees implies refrection across the line y = x and will result in a triangle with vertices where the signs of the original vertices are changed.
Thus, the vertices of the triangle after a 180 degrees rotation are (5, -4), (7, -2) and (2, -3) respectively.

Refrection over the y-axis will result in a triangle with the signs of the x-value of the vertices changed.
Thus, the vertices of the triangle after a refrection over the y-axis are (-5, -4), (-7, -2) and (-2, -3)

Similarly, refrection over the x-axis will result in a triangle with the signs of the y-value of the vertices changed.
Thus, the vertices of the triangle after a refrection over the x-axis are (-5, 4), (-7, 2) and (-2, 3)

Therefore, point A' will lie at (-5, 4) after a series of transformation involving rotation by 180 degrees, refrection over the y-axis and refrection over the x-axs.