Question

Square A"B"C"D" is the final image after the rule T-4-1 OR (x.y) was applied to square ABCD. what is the coordinates of A of square ABCD

Answer 1

The coordinates of A are (2, -1)

Step-by-step explanation

Square A''B''C''D'' is

To transform square ABCD first do a rotation about the origin of 90°. The rule for this transformation is:

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

And then a translation 4 units lefts and 1 unit down.

In this case we have to perform the transformations backwards, to find square ABCD. First we have to reverse the translation, so we have to move the square A''B''C''D'' 4 units right and 1 unit up:

Now we have to rotate square A'B'C'D' 90° about the origin, but counter-clockwise. The rule in this case is:

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

Therefore, the vertices of square ABCD are:

`\begin{gathered} A^(\prime)(-1,-2)\to A(2,-1) \\ B^(\prime)(1,0)\to B(0,1) \\ C^(\prime)(3,-2)\to C(2,3) \\ D^(\prime)(1,-4)\to D(4,1) \end{gathered}`

Therefore, the coordinates of A in square ABCD are (2, -1)