High School

Write down the translation vector which maps:

(a) Flag [tex]\( A \)[/tex] onto Flag [tex]\( B \)[/tex], [tex]\((4,4)\)[/tex].

(b) Flag [tex]\( A \)[/tex] onto Flag [tex]\( C \)[/tex], [tex]\((-6,1)\)[/tex].

(c) Flag [tex]\( A \)[/tex] onto Flag [tex]\( D \)[/tex].

(d) Flag [tex]\( A \)[/tex] onto Flag [tex]\( E \)[/tex].

(e) Flag [tex]\( A \)[/tex] onto Flag [tex]\( F \)[/tex].

(f) Flag [tex]\( A \)[/tex] onto Flag [tex]\( G \)[/tex].

(g) Flag [tex]\( C \)[/tex] onto Flag [tex]\( E \)[/tex].

(h) Flag [tex]\( G \)[/tex] onto Flag [tex]\( B \)[/tex].

(i) Flag [tex]\( B \)[/tex] onto Flag [tex]\( F \)[/tex].

(j) Flag [tex]\( B \)[/tex] onto Flag [tex]\( D \)[/tex].

Answer :

Let's go through the translation vectors for mapping Flags as given:

(a) Flag A onto Flag B:
The translation vector is [tex]\((4, 4)\)[/tex]. This means to map Flag A onto Flag B, you move 4 units to the right and 4 units up.

(b) Flag A onto Flag C:
The translation vector is [tex]\((-6, 1)\)[/tex]. To map Flag A onto Flag C, you move 6 units to the left and 1 unit up.

For the other mappings (c) through (j), there is no information provided on their translation vectors. Therefore, we do not have specific translation vectors to cover those mappings.

When dealing with translation vectors, each vector is expressed in the form [tex]\((x, y)\)[/tex], where [tex]\(x\)[/tex] represents the horizontal shift and [tex]\(y\)[/tex] represents the vertical shift. A positive [tex]\(x\)[/tex] moves the object to the right, a negative [tex]\(x\)[/tex] moves it to the left, a positive [tex]\(y\)[/tex] moves it up, and a negative [tex]\(y\)[/tex] moves it down. If you have the specific coordinates or relative positions for the remaining flags, we can determine their respective translation vectors.