Question

Rectangle PQRS is graphed on a coordinate plane with vertices P(–2, 1), Q(–2, 4), R(–4, 4), and S(–4, 1). Rectangle PQRS is reflected over the y–axis and then translated 2 units to the left resulting in Rectangle P'Q'R'S'. What are the coordinates of P'?

A) (–4, –1)
B) (0, 1)
C) (1, 0)
D) (4, 1)

Answer 1

To find the coordinates of P' when rectangle PQRS is reflected over the y-axis and then translated 2 units to the left, we need to perform two transformations: reflection and translation.

Step-by-step explanation:

To find the coordinates of P' when rectangle PQRS is reflected over the y-axis and then translated 2 units to the left, we need to perform two transformations: reflection and translation.

1. To reflect a point over the y-axis, we change the sign of the x-coordinate. So the new x-coordinate of P' would be the negative of the original x-coordinate of P, which is -(-2) = 2.
2. After reflecting, we need to translate the point 2 units to the left. This means subtracting 2 from the new x-coordinate. So the final x-coordinate of P' would be 2 - 2 = 0.
3. The y-coordinate of P' remains the same as the y-coordinate of P, which is 1.

Therefore, the coordinates of P' are (0, 1).