Answered

Welcome to Westonci.ca, the Q&A platform where your questions are met with detailed answers from experienced experts. Explore our Q&A platform to find in-depth answers from a wide range of experts in different fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Solve for [tex]\( x \)[/tex].

[tex]\[ 3x = 6x - 2 \][/tex]

---

(02.01 LC)

[tex]\[ \triangle DOG \][/tex] has coordinates [tex]\( D(3,2), O(2,-4), \)[/tex] and [tex]\( G(-1,-1) \)[/tex]. A translation maps point [tex]\( D \)[/tex] to [tex]\( D^{\prime}(2,4) \)[/tex]. Find the coordinates of [tex]\( O^{\prime} \)[/tex] and [tex]\( G^{\prime} \)[/tex] under this translation.

A. [tex]\( O^{\prime}(-1,1) ; G^{\prime}(1,-2) \)[/tex]

B. [tex]\( O^{\prime}(0,-3) ; G^{\prime}(-3,0) \)[/tex]

C. [tex]\( O^{\prime}(1,-2) ; G^{\prime}(-2,1) \)[/tex]

D. [tex]\( O^{\prime}(3,0) ; G^{\prime}(-1,-1) \)[/tex]

Sagot :

GinnyAnswer
To find the coordinates of [tex]\(O'\)[/tex] and [tex]\(G'\)[/tex] under the given translation, follow these steps:

1. Identify the translation vector:
- We need to translate point [tex]\(D(3,2)\)[/tex] to [tex]\(D'(2,4)\)[/tex].
- Calculate the translation vector by subtracting the coordinates of [tex]\(D\)[/tex] from [tex]\(D'\)[/tex]:
[tex]\[ \text{Translation vector} = (2 - 3, 4 - 2) = (-1, 2) \][/tex]

2. Apply the translation vector to point [tex]\(O\)[/tex]:
- The initial coordinates of [tex]\(O\)[/tex] are [tex]\(O(2, -4)\)[/tex].
- Add the translation vector [tex]\((-1, 2)\)[/tex] to the coordinates of [tex]\(O\)[/tex]:
[tex]\[ O' = (2 + (-1), -4 + 2) = (1, -2) \][/tex]

3. Apply the translation vector to point [tex]\(G\)[/tex]:
- The initial coordinates of [tex]\(G\)[/tex] are [tex]\(G(-1, -1)\)[/tex].
- Add the translation vector [tex]\((-1, 2)\)[/tex] to the coordinates of [tex]\(G\)[/tex]:
[tex]\[ G' = (-1 + (-1), -1 + 2) = (-2, 1) \][/tex]

Hence, the coordinates of [tex]\(O'\)[/tex] and [tex]\(G'\)[/tex] after the translation are [tex]\(O'(1, -2)\)[/tex] and [tex]\(G'(-2, 1)\)[/tex] respectively.

Therefore, the correct answer is:
[tex]\[ O'(1, -2); G'(-2, 1) \][/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.