Question

Find the composition of transformations that map ABD to EHGF.

Answer 1

Looking at the orientation of each figure, first we need a reflection over the y-axis, this way the orientation of ABCD will match the orientation of EHGF.

After this reflection, the position of each point will be:

(To find the position after a reflection over the y-axis, we need to switch the signal of the x-coordinates)

`\begin{gathered} A^(\prime)(5,2)\\ \\ B^(\prime)(3,4)\\ \\ C^(\prime)(2,4)\\ \\ D^(\prime)(1,2)\\ \end{gathered}`

Now, let's write the coordinates of EHGF:

`\begin{gathered} E(1,-2)\\ \\ H(-1,0)\\ \\ G(-2,0)\\ \\ F(-3,-2) \end{gathered}`

Comparing each corresponding pair of points, we can see that in order to map A'B'C'D' into EHGF, we need to decrease the x-coordinates by 4 units and decrease the y-coordinates by 4 units:

`(x,y)\rightarrow(x+(-4),y+(-4))`

Therefore the answers are y, -4 and -4.