Question

Rectangle PQRS has vertices P(1, 4), Q(6, 4), R(6, 1), and S(1, 1). Without graphing, find the new coordinates of the vertices of the rectangle after a reflection over the x-axis and then another reflection over the y-axis.

Answer 1

P(1, 4), Q(6, 4), R(6, 1), and S(1, 1)

New coordinates of the rectangle after a reflection over the x-axis is:

P'(1, -4), Q'(6, -4), R'(6, -1), and S'(1, -1)

New coordinates of the rectangle after a reflection over the y-axis is:

P"(-1, 4), Q"(-6, 4), R"(-6, 1), and S"(-1, 1)

.

Answer 2

Over the Y axis.

P(-1, 4), Q(-6, 4), R(-6, 1), and S(-1, 1)

Over the X axis:

P(1, -4), Q(6, -4), R(6, -1), and S(1, -1)

Explanation:

In order to finde the new coordinates after a reflection on the Y or X axis, you just have to change the sign of the opposite variable, for example if you want to reflect the points on the Y axis you change the signs of all the X´s on the points, and the same with the reflections of the X axis, you have to change the signs of all the Y´s on the points.