Question

If a triangle with vertices (4, 3)
, (8, 3)
, and (7, 5)
is translated to the right 4 units and down 2 units, what are the vertices of the translated figure?(1 point)
Responses

(8, 1)
, (12, 1)
, and (11, 3)
left parenthesis 8 comma 1 right parenthesis , left parenthesis 12 comma 1 right parenthesis , and left parenthesis 11 comma 3 right parenthesis

(0, 1)
, (4, 1)
, and (3, 3)
left parenthesis 0 comma 1 right parenthesis , left parenthesis 4 comma 1 right parenthesis , and left parenthesis 3 comma 3 right parenthesis

(8, 3)
, (12, 3)
, and (11, 5)
left parenthesis 8 comma 3 right parenthesis , left parenthesis 12 comma 3 right parenthesis , and left parenthesis 11 comma 5 right parenthesis

(8, 5)
, (12, 5)
, and (11, 7)

Answer 1

To find the new vertices of the triangle after translating it 4 units to the right and 2 units down, we need to apply the translation to each of the original vertices.

The original vertices are:
1. (4, 3)
2. (8, 3)
3. (7, 5)

### Translation Steps:
1. Translate right 4 units:
- For point (x, y), the new x-coordinate will be \(x + 4\).
2. Translate down 2 units:
- For point (x, y), the new y-coordinate will be \(y - 2\).

### Calculate the new vertices:
1. For the vertex (4, 3):
- New x: \(4 + 4 = 8\)
- New y: \(3 - 2 = 1\)
- Translated point: (8, 1)

2. For the vertex (8, 3):
- New x: \(8 + 4 = 12\)
- New y: \(3 - 2 = 1\)
- Translated point: (12, 1)

3. For the vertex (7, 5):
- New x: \(7 + 4 = 11\)
- New y: \(5 - 2 = 3\)
- Translated point: (11, 3)

### Translated vertices:
So the translated vertices are:
- (8, 1)
- (12, 1)
- (11, 3)

The correct response is:
**(8, 1), (12, 1), and (11, 3)**.