Question

Choose the possible dilation image of the following figure.

• A.
• B.
• C. Both option A and B.
• D. None of the above.

Answer 1

The correct option is B

In dilated shape, each of the coordinate points of the original figure gets multiplied by a constant scale factor.

Hence, if any point of the original figure lies at the origin then its corresponding coordinate point is zero.

To dilate this particular point we multiply with the scale factor.
$\Rightarrow \text{New coordinate point}=\text{Original coordinate point}\times \text{scale factor}$
$\Rightarrow \text{New coordinate point}=0\times \text{scale factor}$
$\Rightarrow \text{New coordinate point}=0$

$\therefore$ It can be inferred that if a figure lies over the origin, then it must lie over the origin even after dilation.

Corollary of the above statement is
$\to$ If a figure does not lie or touch the origin before dilation, it should not do so after dilation as well.

Hence, in the provided figure as the circle does not lie or touch the origin, it must not lie or touch the origin after dilation.

$\therefore$ The below image is a possible dilated image of the original figure.