Question

has coordinates Upper M left parenthesis 5 comma negative 1 right parenthesis​, Upper U left parenthesis 6 comma 8 right parenthesis​, and Upper G left parenthesis 2 comma negative 2 right parenthesis. A translation maps point M to Upper M prime left parenthesis 2 comma 1 right parenthesis. What are the coordinates of Upper U prime and Upper G prime for this​ translation?
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Part 1
Upper U prime nothing
  
​(Type an ordered​ pair.)

Answer 1

To find the coordinates of \( U' \) and \( G' \) after the translation that maps point \( M \) to \( M' \), we first need to determine the translation vector.

The original coordinates of \( M \) are \( (5, -1) \) and the new coordinates \( M' \) are \( (2, 1) \). To find the translation vector, we subtract the coordinates of \( M \) from those of \( M' \):

\[
\text{Translation vector} = M' - M = (2 - 5, 1 - (-1)) = (-3, 2).
\]

This means that the translation moves each point 3 units to the left and 2 units up.

Now, we will apply this translation vector to the coordinates of \( U(6, 8) \) and \( G(2, -2) \).

1. **Finding \( U' \)**:
\[
U' = U + \text{Translation vector} = (6, 8) + (-3, 2) = (6 - 3, 8 + 2) = (3, 10).
\]

2. **Finding \( G' \)**:
\[
G' = G + \text{Translation vector} = (2, -2) + (-3, 2) = (2 - 3, -2 + 2) = (-1, 0).
\]

Thus, the coordinates for \( U' \) are:

\[
U' = (3, 10).
\]

If you need to provide the coordinates for \( U' \):

**Part 1**: \( U' = (3, 10) \)