Sure! Let's go through the translation process step by step for each vertex of the quadrilateral CARD.
The original coordinates of the vertices are:
- C(5, -3)
- A(9, -3)
- R(11, -7)
- D(3, -7)
The translation involves moving each vertex three units to the right and eight units up. This means we add 3 to the x-coordinate and 8 to the y-coordinate of each vertex.
1. Translating Vertex C(5, -3):
- New x-coordinate: [tex]\( 5 + 3 = 8 \)[/tex]
- New y-coordinate: [tex]\( -3 + 8 = 5 \)[/tex]
- So, the new coordinates for C are (8, 5).
2. Translating Vertex A(9, -3):
- New x-coordinate: [tex]\( 9 + 3 = 12 \)[/tex]
- New y-coordinate: [tex]\( -3 + 8 = 5 \)[/tex]
- So, the new coordinates for A are (12, 5).
3. Translating Vertex R(11, -7):
- New x-coordinate: [tex]\( 11 + 3 = 14 \)[/tex]
- New y-coordinate: [tex]\( -7 + 8 = 1 \)[/tex]
- So, the new coordinates for R are (14, 1).
4. Translating Vertex D(3, -7):
- New x-coordinate: [tex]\( 3 + 3 = 6 \)[/tex]
- New y-coordinate: [tex]\( -7 + 8 = 1 \)[/tex]
- So, the new coordinates for D are (6, 1).
Thus, after translating the quadrilateral CARD three units to the right and eight units up, the new coordinates of the vertices are:
- C'(8, 5)
- A'(12, 5)
- R'(14, 1)
- D'(6, 1)
These are the coordinates of the images of each vertex after the translation.
