Question

Pentagon ABCDE and pentagon A'B'C'D'E' are shown on the coordinate plane below: Pentagon ABCDE and pentagon A prime B prime C prime D prime E prime on the coordinate plane with ordered pairs at A negative 4, 5, at B negative 6, 4, at C negative 5, 1, at D negative 2, 2, at E negative 2, 4, at A prime 4, negative 7, at B prime 2, negative 6, at C prime 3, negative 3, at D prime 6, negative 4, at E prime 6, negative 6. Which two transformations are applied to pentagon ABCDE to create A'B'C'D'E'?

Answer 1

A reflection across the x-axis and a translation (x + 8, y -2)

Answer 2

Reflection across x- axis and then translation (x+8,y-2).

Explanation:

We are given that a pentagon ABCDE with vertices A at (-4,5), B at (-6,4),C at (-5,1) , D at (-2,2) , E at (-2,4).

The pentagon A'B'C'D'E' is the image of pentagon ABCDE create after transformation.

The vertices A' at (4,-7),B' at (2,-6), C' at (3,-3), D' at (6,-4) and E' at (6,-6).

We have to find the transformation applied on pentagon ABCDE to create A'B'C'D'E'.

The rule of transformation of reflection across x- axis is given by

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

Therefore, the coordinates of ABCDE after reflection across x- axis is given by

`A =(-4,5)\rightarrow (-4,-5)`

`B=(-6,4)\rightarrow (-6,-4)`

`C=(-5,1)\rightarrow (-5,-1)`

`D=(-2,2)\rightarrow (-2,-2)`

`E=(-2,4)\rightarrow (-2,-4)`

Now, apply the translation

`(x,y)\rightarrow (x+8, y-2)`

Therefore, after applying translation then, we get

`(-4,-5)\rightarrow (4,-7)=A'`

`(-6,-4)\rightarrow (2,-6)=B'`

`(-5,-1)\rightarrow (3,-3)=C'`

`(-2,-2)\rightarrow (6,-4)=D'`

`(-2,-4)\rightarrow (6,-6)=E'`

Hence, A'B'C'D'E' is created .

Answer:Reflection across x- axis and then translation (x+8,y-2).