Question

trapezoid H'I'J'K' is the image of trapezoid HIJK under a translation right 5 units up and 4 units followed by a rotation about the origin.write the rules for the translation and rotation.translation (x,y)rotation (x,y)

Answer 1

`\begin{gathered} \text{Translation:}(x,y)\to(x+5,y+4) \\ Rotation\colon(x,y)\to(-x,-y) \end{gathered}`

Explanation:

Given that trapezoid HIJK is translated right 5 units and up 4 units, the translation rule is given as:

`\text{Translation:}(x,y)\to(x+5,y+4)`

Next, to find the rotation rule, we use point H.

• The coordinate of point H = (-6, -9)

After the translation, the new point is given as:

`(-6,-9)\to(-6+5,-9+4)=(-1,-5)_{}`

From the graph, the coordinate of the image point H' = (1, 5).

Observe that the rotation changes the sign on both axes. Thus, the rotation rule is given as:

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