Answered

Explore Westonci.ca, the top Q&A platform where your questions are answered by professionals and enthusiasts alike. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

1. Suppose triangle [tex]\(DEF\)[/tex] has vertices [tex]\(D(3,5)\)[/tex], [tex]\(E(6,-6)\)[/tex], and [tex]\(F(1,3)\)[/tex]. What are the coordinates of [tex]\(D'\)[/tex], [tex]\(E'\)[/tex], and [tex]\(F'\)[/tex] after triangle [tex]\(DEF\)[/tex] is translated 5 units up and 6 units right?

A. [tex]\(D'(9,10)\)[/tex], [tex]\(E'(12,-1)\)[/tex], [tex]\(F'(7,8)\)[/tex]

B. [tex]\(D'(9,10)\)[/tex], [tex]\(E'(0,-1)\)[/tex], [tex]\(F'(7,-2)\)[/tex]

C. [tex]\(D'(-3,10)\)[/tex], [tex]\(E'(0,-1)\)[/tex], [tex]\(F'(-5,8)\)[/tex]

D. [tex]\(D'(-3,0)\)[/tex], [tex]\(E'(0,-11)\)[/tex], [tex]\(F'(-5,-2)\)[/tex]

Sagot :

GinnyAnswer
To determine the new coordinates of the vertices [tex]\( D, E, \)[/tex] and [tex]\( F \)[/tex] after translating the triangle [tex]\( DEF \)[/tex] 5 units up and 6 units to the right, we follow these steps:

1. Identify the initial coordinates:
- [tex]\( D(3, 5) \)[/tex]
- [tex]\( E(6, -6) \)[/tex]
- [tex]\( F(1, 3) \)[/tex]

2. Apply the translation:
- Move each vertex 6 units to the right. This means we add 6 to the x-coordinate of each vertex.
- Move each vertex 5 units up. This means we add 5 to the y-coordinate of each vertex.

3. Calculate the new coordinates:
- For vertex [tex]\( D(3, 5) \)[/tex]:
- New x-coordinate: [tex]\( 3 + 6 = 9 \)[/tex]
- New y-coordinate: [tex]\( 5 + 5 = 10 \)[/tex]
- New coordinates of [tex]\( D \)[/tex] are [tex]\( D(9, 10) \)[/tex].

- For vertex [tex]\( E(6, -6) \)[/tex]:
- New x-coordinate: [tex]\( 6 + 6 = 12 \)[/tex]
- New y-coordinate: [tex]\( -6 + 5 = -1 \)[/tex]
- New coordinates of [tex]\( E \)[/tex] are [tex]\( E(12, -1) \)[/tex].

- For vertex [tex]\( F(1, 3) \)[/tex]:
- New x-coordinate: [tex]\( 1 + 6 = 7 \)[/tex]
- New y-coordinate: [tex]\( 3 + 5 = 8 \)[/tex]
- New coordinates of [tex]\( F \)[/tex] are [tex]\( F(7, 8) \)[/tex].

4. Summarize the new coordinates:
- [tex]\( D(9, 10) \)[/tex]
- [tex]\( E(12, -1) \)[/tex]
- [tex]\( F(7, 8) \)[/tex]

Therefore, after translating the triangle 5 units up and 6 units to the right, the new coordinates of [tex]\( D, E, \)[/tex] and [tex]\( F \)[/tex] are [tex]\( D(9, 10) \)[/tex], [tex]\( E(12, -1) \)[/tex], and [tex]\( F(7, 8) \)[/tex].

Hence, the correct option is:
[tex]\[ D_c(9,10), E_c(12,-1), F_c(7,8) \][/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.