Question

your turn
the figures shown are congruent. find a rigid motion that maps one figure to the other. give coordinate - notation for the transformations you use.

1. (abcdcong wxyz)

part 1: figure (abcd) can be mapped onto (wxyz) by...
□ a rotation
□ b reflection
□ c translation
□ d the figures are not congruent.
part 2: the coordinate notation is

1. (abcdecong pqrst)

part 1: (abcde) can be mapped onto (pqrst) by...
□ a rotation
□ b reflection
□ c translation
□ d the figures are not congruent.
part 2: the coordinate notation is

Explanation:

Step1: Analyze figure ABCD and WXYZ

By observing the orientation and position of the two - congruent figures ABCD and WXYZ, we can see that one figure can be obtained from the other by moving it without rotating or reflecting. This is a translation.

Step2: Determine the translation rule

Let's take a vertex of ABCD, say A(4, 6). Its corresponding vertex in WXYZ is W(4, - 2). The x - coordinate remains the same and the y - coordinate changes by \(6-( - 2)=8\) units down. The coordinate notation for a translation is \((x,y)\to(x,y - 8)\).

Step3: Analyze figure ABCDE and PQRST

By observing the orientation and position of the two - congruent figures ABCDE and PQRST, we can see that one figure can be obtained from the other by moving it without rotating or reflecting. This is a translation.

Step4: Determine the translation rule for ABCDE and PQRST

Let's take a vertex of ABCDE, say A(2, 6). Its corresponding vertex in PQRST is P(2, - 2). The x - coordinate remains the same and the y - coordinate changes by \(6-( - 2)=8\) units down. The coordinate notation for a translation is \((x,y)\to(x,y - 8)\).

Answer:

1.
Part 1: C Translation
Part 2: \((x,y)\to(x,y - 8)\)
2.
Part 1: C Translation
Part 2: \((x,y)\to(x,y - 8)\)