Westonci.ca connects you with experts who provide insightful answers to your questions. Join us today and start learning! Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

The coordinates of the vertices of quadrilateral CARD are [tex]\(C(5, -3)\)[/tex], [tex]\(A(9, -3)\)[/tex], [tex]\(R(11, -7)\)[/tex], and [tex]\(D(3, -7)\)[/tex]. If this quadrilateral is translated three units to the right and eight units up, what are the coordinates of the images of each vertex?

Sagot :

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.