Question

A shape is rotated about the origin. The initial coordinates of a point on the shape, the final coordinates of the same point on the shape, and the degree of rotation by which the shape has been rotated about the origin are mentioned in each option.
Which of the following options contains the correct combination?

• A. $\begin{array}{ccc}\text{Initial coordinates}& \text{Final coordinates}& \text{Rotation}\\ (4,0)& (0,4)& {90}^{\circ }\text{counterclockwise rotation}\end{array}$
• B. All of the above
• C. $\begin{array}{ccc}\text{Initial coordinates}& \text{Final coordinates}& \text{Rotation}\\ (4,0)& (0,4)& {270}^{\circ }\text{clockwise rotation}\end{array}$
  
• D. $\begin{array}{ccc}\text{Initial coordinates}& \text{Final coordinates}& \text{Rotation}\\ (4,0)& (-4,0)& {180}^{\circ }\text{counterclockwise rotation}\end{array}$

Answer 1

The correct option is B All of the above

Option A
The rotation of point (4, 0) by ${90}^{\circ }$ in the counterclockwise direction is illustrated in the image shown below.

From the image shown above, we can observe that the coordinates of the point obtained by the rotation of point (4, 0) by ${90}^{\circ }$ in the counterclockwise direction are (0, 4).
Option B
The rotation of the point (4, 0) by ${180}^{\circ }$ in the counterclockwise direction is illustrated in the image shown below.

From the image shown above, we can observe that the coordinates of the point obtained by the rotation of point (4, 0) by ${90}^{\circ }$ in the counterclockwise direction are (-4, 0).
Option C
The rotation of point (4, 0) by ${270}^{\circ }$ in the clockwise direction is illustrated in the image shown below.
From the image shown above, we can observe that the coordinates of the point obtained by the rotation of point (4, 0) by ${90}^{\circ }$ in the counterclockwise direction are (0, 4).
$\to$ Option D is correct.