Question

Write a series of rigid motions that transform pentagon ABCDE to pentagon A′B′C′D′E′

Answer 1

We need the following three rigid motions:

i) Reflection around y-axis, ii) Translation three units in the -y direction, iii) Translation four units in the -x direction.

Explanation:

We need to perform three operations on pentagon ABCDE to create pentagon A'B'C'D'E':

i) Reflection around y-axis:

`(x',y') = (-x,y)` (Eq. 1)

ii) Translation three units in the -y direction:

`(x'',y'') = (x', y'-3)` (Eq. 2)

iii) Translation four units in the -x direction:

`(x''',y''') = (x''-4, y'')` (Eq. 3)

We proceed to proof the effectiveness of operations defined above by testing point D:

1)
`D(x,y) = (-1, 4)` Given.

2)
`(x',y') = (1,4)` By (Eq. 1)

3)
`(x'',y'') = (1, 1)` By (Eq. 2)

4)
`D'(x,y) = (-3,1)` By (Eq. 3)/Result