Question: The rectangle is resized by a factor of 2 with central point (0, 0), then resized again by a factor ...

Question

The rectangle is resized by a factor of 2 with central point (0, 0), then resized again by a factor of 0.5 with central point (2, 0). Which one of the following shows the correct image?

(a)

(b)

(c)

(d)

Answer 1

Solution

Here, first we have to examine the figures carefully then write down the description for each figure regarding the factor and centre before and after resizing which will help us to get a clear picture of our answer.

Complete step-by-step answer:
Here, in figure (a):

If you carefully look at the above figure, you will see that EFGH is a resizing of the original figure by a factor of 2 with central point $\left( 0,0 \right)$ and then ABCD is a resizing by a factor of 0.5 with central point $\left( 2,0 \right)$ .
In figure (b),

ABCD shows a resizing of the original by a factor of 0.5 with central point $\left( 2,0 \right)$ followed by the resizing of ABCD which gives EFGH by a factor of 2 with central point $\left( 0,0 \right)$ .
So now, in (c),

In the above figure, we can see that EFGH is resizing by a factor of 2 with central point $\left( 2,0 \right)$ then resized by a factor of 0.5 with central point $\left( 0,0 \right)$ .
Similarly, in figure (d)

In the above figure, you can see that ABCD is a resized of the original by a factor of 0.5 with central point $\left( 2,0 \right)$ and then EFGH is the resized by a factor of 2 with central point $\left( 2,0 \right)$ .
Therefore, we can say that figure (a) is the rectangle that is resized by a factor of 2 with central point $\left( 0,0 \right)$ , then again resized by a factor of 0.5 with central point $\left( 2,0 \right)$ .

So, the correct answer is “Option (a)”.

Note: Here, resizing means the shape getting bigger or smaller. Resizing not only requires a scale or a factor but also a centre point of origin. Here, you can consider resizing as a torch shining from the centre point to the rectangle and the resize depending on the scale.
The important point to be noted here is that the cross $\left( + \right)$ sign in the figures, represents the central point of the final resized figure.