Rotations Quick Check

Question

4 of 54 of 5 Items
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, 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)
left parenthesis 8 comma 5 right parenthesis , left parenthesis 12 comma 5 right parenthesis , and left parenthesis 11 comma 7 right parenthesis

(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)

Answer 1

To find the new vertices of the triangle after the translation, we need to apply the translation rules to each vertex of the triangle.

The original vertices of the triangle are:

• \( (4, 3) \)
• \( (8, 3) \)
• \( (7, 5) \)

The translation is to the right 4 units and down 2 units.

To apply this translation:

1. To translate to the right 4 units, we add 4 to the x-coordinate of each vertex.
2. To translate down 2 units, we subtract 2 from the y-coordinate of each vertex.

Now, let's calculate the new coordinates for each vertex:

1. For the vertex \( (4, 3) \):

   • New x-coordinate: \( 4 + 4 = 8 \)
   • New y-coordinate: \( 3 - 2 = 1 \)
   • Translated vertex: \( (8, 1) \)

2. For the vertex \( (8, 3) \):

   • New x-coordinate: \( 8 + 4 = 12 \)
   • New y-coordinate: \( 3 - 2 = 1 \)
   • Translated vertex: \( (12, 1) \)

3. For the vertex \( (7, 5) \):

   • New x-coordinate: \( 7 + 4 = 11 \)
   • New y-coordinate: \( 5 - 2 = 3 \)
   • Translated vertex: \( (11, 3) \)

Now, we have the new vertices after translation:

• \( (8, 1) \)
• \( (12, 1) \)
• \( (11, 3) \)

Thus, the correct response is: \( (8, 1), (12, 1), \) and \( (11, 3) \).