Question

Which of the following coordinate points have undergone an enlargement and reduction? Select all that apply.Group of answer choices(5, -1) --> (10, 2) --> (20, 4)(1, 1) --> (6, 6) --> (1, 1)(4, 9) --> (20, 34) --> (20/45, 1)(3, 0) --> (9, 0) --> (18, 0)(0, -5) --> (0, 5) --> (0, 30)

Answer 1

By definition, you know that dilations have a scale factor, this is labeled k. To dilate something in the coordinate plane, multiply each coordinate by the scale factor.

If there is a reduction, then 0 < k < 1.

If there is an enlargement, then k > 1.

`(x,y)\rightarrow(kx,ky)`

So, you have

`\begin{gathered} (5,-1)\rightarrow(5\cdot2,-1\cdot-2)=(10,2) \\ \text{ k is not the same for both coordinates of the point} \end{gathered}`

`\begin{gathered} (1,1)\rightarrow(6\cdot1,6\cdot1)=(6,6) \\ \text{In this case, k = 6 and k > 1 then the coordinate points have an enlargement} \\ (6,6)\rightarrow((1)/(6)\cdot6,(1)/(6)\cdot6)=(1,1) \\ \text{In this case, k = 1 and 0< k < 1 then the coordinate points have an reduction} \end{gathered}`
`\begin{gathered} (4,9)\rightarrow(4\cdot5,9\cdot(34)/(9))=(20,34) \\ \text{ k is not the same for both coordinates of the point} \end{gathered}`
`\begin{gathered} (3,0)\rightarrow(3\cdot3,3\cdot0)=(9,0) \\ \text{In this case, k = 3 and k > 1 then the coordinate points have an enlargement} \\ (9,0)\rightarrow(2\cdot9,2\cdot0)=(18,0) \\ \text{In this case, k = 2 and k > 1 then the coordinate points have an enlargement} \end{gathered}`

Therefore, the correct answer is

`B\text{.}(1,1)\rightarrow(6,6)\rightarrow(1,1)`