Question

I need help with this geometry question can someone please help

Answer 1

We are asked to determine the sequence of transformations necessary to go from figure 1 to figure 2. First, we will label all the vertices points in figure 1, like this:

Now we will apply a 90 degrees rotation counterclockwise above the origin. This transformation is done applying the following rule:

$(x,y)\rightarrow(-y,x)$

Therefore, applying the rule to the first point we get:

$(5,2)\rightarrow(-2,5)$

For the second point we get:

$(8,5)\rightarrow(-5,8)$

And for the third point we get:

$(5,7)\rightarrow(-7,5)$

Now we will plot the new figure using the point we found, we get:

Now we see that the next transformation is to translate the figure 3 units down to get figure 1. Therefore, the transformations to be made are a 90 degrees rotation counterclockwise and a translation 3 units down.