Question

Use the graph and the translation left parenthesis x comma y right parenthesis right arrow left parenthesis x plus 3 comma y plus 1 right parenthesis to answer parts a and b below.
-5
3
-10
6
4
-5
8
x
y
A
B
C



interactive graph
Question content area bottom
Part 1
a. Enter the image of each vertex as an ordered pair.
Upper A right arrow Upper A prime nothing
  
Upper B right arrow Upper B prime nothing
  
Upper C right arrow Upper C prime nothing
  
​(Type ordered​ pairs.)
A(-8,5) B(-1,0) C(-3,-2)

Answer 1

To apply the translation \((x, y) \rightarrow (x + 3, y + 1)\) to each of the vertices A, B, and C, we will add 3 to the x-coordinate and 1 to the y-coordinate of each vertex.

1. For vertex A \((-8, 5)\):
\[
A' = (-8 + 3, 5 + 1) = (-5, 6)
\]

2. For vertex B \((-1, 0)\):
\[
B' = (-1 + 3, 0 + 1) = (2, 1)
\]

3. For vertex C \((-3, -2)\):
\[
C' = (-3 + 3, -2 + 1) = (0, -1)
\]

Now we can summarize the transformed vertices:

- \( A' = (-5, 6) \)
- \( B' = (2, 1) \)
- \( C' = (0, -1) \)

So the answers are:

- \( A' = (-5, 6) \)
- \( B' = (2, 1) \)
- \( C' = (0, -1) \)