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2. The vertices of a triangle are located at points [tex]\(A(-2,-1), B(1,3)\)[/tex], and [tex]\(C(2,-4)\)[/tex]. The triangle is translated 3 units right and 1 unit up. What are the coordinates of the vertices of triangle [tex]\(A^{\prime} B^{\prime} C^{\prime}\)[/tex]?

A. [tex]\(A^{\prime}(-3,0), B^{\prime}(0,4), C^{\prime}(1,-3)\)[/tex]

B. [tex]\(A^{\prime}(1,0), B^{\prime}(2,6), C^{\prime}(3,-1)\)[/tex]

C. [tex]\(A^{\prime}(1,0), B^{\prime}(4,4), C^{\prime}(5,-3)\)[/tex]

D. [tex]\(A^{\prime}(-5,-2), B^{\prime}(-2, k), C^{\prime}(-1,-7)\)[/tex]



Answer :

GinnyAnswer
To solve this translation problem, let's apply the translation to each vertex of the triangle step by step.

We start with the original vertices:
- [tex]\( A(-2, -1) \)[/tex]
- [tex]\( B(1, 3) \)[/tex]
- [tex]\( C(2, -4) \)[/tex]

The translation specifies moving the points 3 units to the right and 1 unit up.

### Translation of Point [tex]\(A\)[/tex]:
- Original coordinates: [tex]\( A(-2, -1) \)[/tex]
- Translate 3 units to the right: [tex]\( -2 + 3 = 1 \)[/tex]
- Translate 1 unit up: [tex]\( -1 + 1 = 0 \)[/tex]
- New coordinates: [tex]\( A'(1, 0) \)[/tex]

### Translation of Point [tex]\(B\)[/tex]:
- Original coordinates: [tex]\( B(1, 3) \)[/tex]
- Translate 3 units to the right: [tex]\( 1 + 3 = 4 \)[/tex]
- Translate 1 unit up: [tex]\( 3 + 1 = 4 \)[/tex]
- New coordinates: [tex]\( B'(4, 4) \)[/tex]

### Translation of Point [tex]\(C\)[/tex]:
- Original coordinates: [tex]\( C(2, -4) \)[/tex]
- Translate 3 units to the right: [tex]\( 2 + 3 = 5 \)[/tex]
- Translate 1 unit up: [tex]\( -4 + 1 = -3 \)[/tex]
- New coordinates: [tex]\( C'(5, -3) \)[/tex]

So, the new coordinates of the vertices of the triangle after the translation are:
- [tex]\( A'(1, 0) \)[/tex]
- [tex]\( B'(4, 4) \)[/tex]
- [tex]\( C'(5, -3) \)[/tex]

The correct answer is:
[tex]\[ A'(1, 0), B'(4, 4), C'(5, -3) \][/tex]

Therefore, the correct option from the given choices is:
[tex]\[ \boxed{A'(1, 0), B'(4, 4), C'(5, -3)} \][/tex]

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