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 (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 (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)

Answer 1

To translate a point in the coordinate plane, you add (or subtract) from the x-coordinate and y-coordinate. In this case, we are translating the triangle to the right 4 units (add 4 to the x-coordinates) and down 2 units (subtract 2 from the y-coordinates).

Let's calculate the new coordinates of each vertex:

1. For the vertex (4, 3):

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

2. For the vertex (8, 3):

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

3. For the vertex (7, 5):

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

Therefore, the vertices of the translated triangle are \( (8, 1) \), \( (12, 1) \), and \( (11, 3) \).

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