Question

Rotate point R(4,−1) and S(3,1) by 90 degrees about the origin.

a) R(−1,−4),S(−1,−3)
b) R(1,4),S(1,3)
c) R(1,−4),S(1,−3)
d) R(−1,4),S(−1,3)

Answer 1

When rotating points R(4, -1) and S(3, 1) by 90 degrees counterclockwise about the origin, the new coordinates become R(-1, 4) and S(-1, 3), which makes answer d) the correct option.

Step-by-step explanation:

The student is asking how to rotate points R(4, -1) and S(3, 1) by 90 degrees about the origin. When you rotate a point (x, y) by 90 degrees counterclockwise, the new coordinates can be given by (-y, x). Applying this to point R, the new coordinates after rotation would be R'(-(-1), 4) which simplifies to R'(1, 4). For point S, the new coordinates would be S'(-1, 3). Therefore, the correct answer is d) R(-1, 4), S(-1, 3).

In terms of the mathematical relations to express the new coordinates after a rotation, x' = -y and y' = x are used for a 90-degree counterclockwise rotation. Conversely, x' = y and y' = -x would be applied for a 90-degree clockwise rotation. These transformations ensure the distance of a point to the origin remains invariant under rotation, which satisfies the equation x'^2 + y'^2 = x^2 + y^2.