Question

Determine a series of transformations that would map Figure H onto Figure I.There are two blanks to choose, each from "reflection", "rotation" and "translation".

Answer 1

We can see that the shapes are the same, so we just need to change the orientation, which we can do rotation, and the position, which we can do by translation.

Firstly, we can see that if we rotate the Figure H by 90° anti-clockwise, we will have both in the same orientation.

Rotation anti-clockwise is better done with respect to the origin, and to do it, we change the sign of the y coordinate and switch the x and y coordinates:

Rotation 90° anti-clockwise:

`(x,y)\to(-y,x)`

We have the vertexes of Figure H at points (-3, 7), (-1, 3), (-2, 2) and (-2, 4), so after the rotation we will have:

Rotation 90° anti-clockwise:

`\begin{gathered} (-3,7)\to(-7,-3) \\ (-1,3)\to(-3,-1) \\ (-2,2)\to(-2,-2) \\ (-2,4)\to(-4,-2) \end{gathered}`

We will get this:

Now, we have the figure in the same orientation, so we just need to translate it. We can pick one of the vertexes as reference, let's pick the (-7, -3). We want to translate it from (-7, -3) to (0, -3), so we can do a translation to the right by 7 units, which we do by adding 7 to the x coordinates:

Trnaslation 7 units right: