Consider a circle with its centre at the origin (O), as shown. Two operations are allowed on the circle. Operation 1: Scale independently along the x and y axes. Operation 2: Rotation in any direction about the origin. Which figure among the options can be achieved through a combination of these two operations on the given circle?
To determine which figure can be achieved through the given operations on the circle, let's analyze the operations in detail:
- Operation 1: Scale independently along the x and y axes.
- This operation allows us to change the dimensions of the circle along the x-axis and y-axis independently. A circle, when scaled differently along two axes, becomes an ellipse.
- Operation 2: Rotation in any direction about the origin.
- This operation allows rotation of the figure around its center at the origin, meaning we can change the orientation of the ellipse formed in the previous step.
From the above operations, we can create an ellipse and rotate it. Therefore, the correct figure among the options is the one that forms an ellipse, as shown below:
Conclusion: The original circle can be transformed into an ellipse through independent scaling along the x and y axes, and the orientation of the ellipse can be changed through rotation.
Important Questions from Shape Transformation
The given figure is reflected about the horizontal dashed line and then rotated clockwise by 90° about an axis perpendicular to the plane of the figure.
Which one of the following options correctly shows the resultant figure?
Note: The figures shown are representative.
- The given figure is reflected about the horizontal dashed line and then rotated clockwise by 90° about an axis perpendicular to the plane of the figure. Which one of the following options correctly shows the resultant figure? Note: The figures shown are representative.
