Question

Rectangle PQRS is rotated 180° about the origin, with the following coordinates: P(5, -5), Q(0, 5), S(0, -5). Before the rotation, the coordinate point of R is (-1, -4). What are the coordinates of R' after the 180-degree rotation?

A) (1, 4)
B) (4, 1)
C) (-4, -1)
D) (-5, 0)

Answer 1

The coordinates of point R' after a 180-degree rotation about the origin are (1, 4), which is option A. This is obtained by applying the rotation transformation equations for a 180-degree turn on the original coordinates of point R (-1, -4).

Step-by-step explanation:

The student asked what are the coordinates of point R' after a 180-degree rotation about the origin, given that before the rotation, the coordinate point of R is (-1, -4). To find the coordinates of R' after the 180-degree rotation, we can use the rotation relations for a 180-degree turn (180 degrees is equivalent to π radians):

• x' = x cos(π) - y sin(π)
• y' = x sin(π) + y cos(π)

Substituting the given coordinates of R and the values for cos(π) and sin(π), which are -1 and 0 respectively, we get:

• x' = (-1)(-1) - (-4)(0) = 1
• y' = (-1)(0) + (-4)(-1) = 4

Therefore, the coordinates of R' after the rotation are (1, 4), which corresponds to option A.