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djverab [1.8K]
3 years ago
9

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

Mathematics
1 answer:
worty [1.4K]3 years ago
7 0

Answer:

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.

Step-by-step 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

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