Question

Enter the ordered pair for the vertices for Rx-axis(QRST).

(A) Q' = (0,0), R' = (1,0), S' = (1,1), T = (0,1)
(B) Q' = (0,0), R' = (1,0), S' = (1,-1), T = (0,-1)
(C) Q' = (0,0), R' = (-1,0), S' = (-1,1), T = (0,1)
(D) Q' = (0,0), R' = (-1,0), S' = (-1,-1), T = (0,-1)

Answer 1

The ordered pair for the vertices for Rx-axis(QRST) is Q' = (0,0), R' = (1,0), S' = (1,1), T' = (0,1).The correct answer (A) accurately reflects the properties of Rx-axis, where Q' is the origin, R' lies on the x-axis, and S' and T' are points in the first quadrant forming a rectangle.

Step-by-step explanation:

The correct option is (A) with the ordered pair for the vertices of Rx-axis as follows: Q' = (0,0), R' = (1,0), S' = (1,1), T' = (0,1). To understand this, let's consider the vertices of a rectangle in a Cartesian coordinate system.

1. Q' = (0,0):The origin, where both x and y coordinates are zero.

2. R' = (1,0): A point on the x-axis where y is zero.

3. S' = (1,1):A point where both x and y coordinates are positive, forming the top-right corner.

4.T' = (0,1): A point where x is zero, and y is positive.

This arrangement corresponds to a rectangle in the first quadrant, with sides parallel to the axes. Options (B), (C), and (D) have incorrect y-coordinates for points S' and T', placing them in different quadrants or on the wrong side of the x-axis. Therefore, option (A) is the correct one.

In summary, the correct answer is (A) because it accurately represents the vertices of a rectangle in the first quadrant of the Cartesian coordinate system. This aligns with the description of Rx-axis (rectangular axis) where the sides are parallel to the coordinate axes.

Answer 2

The correct ordered pair for the vertices for Rx-axis(QRST) is Q' = (0,0), R' = (-1,0), S' = (-1,1), T = (0,1). So, the correct option is (C) Q' = (0,0), R' = (-1,0), S' = (-1,1), T = (0,1).

Step-by-step explanation:

The Rx-axis denotes a rotation of 90 degrees counterclockwise about the origin. In a rotation, the x and y coordinates switch places, but the sign for x changes oppositely.

Considering this, the given vertices are transformed accordingly: Q' = (0,0) remains unchanged as it lies on the origin; R' = (-1,0) is obtained by the x-coordinate changing sign from 1 to -1 while the y-coordinate remains at 0; S' = (-1,1) has the x-coordinate altered to -1 and the y-coordinate changing from 1 to -1; finally, T = (0,1) sees the x and y coordinates switch places, leading to (1,0), and then the x-coordinate is inverted to 0.

This transformation adheres to the rules of rotation about the Rx-axis, validating the correctness of option (C) as the correct ordered pair for the vertices for Rx-axis(QRST). It showcases the necessary adjustment of coordinates following a 90-degree counterclockwise rotation about the origin, aligning with the principles of coordinate transformations within mathematics. Hence, option (C) accurately represents the rotated coordinates of the vertices of Rx-axis(QRST).

So, the correct option is (C) Q' = (0,0), R' = (-1,0), S' = (-1,1), T = (0,1).