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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]
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