To solve this problem, we are given the coordinates of point [tex]\(M\)[/tex] from polygon [tex]\(JKLM\)[/tex], which are [tex]\(M(0, -1)\)[/tex]. We need to determine the new coordinates of point [tex]\(M'\)[/tex] after translating point [tex]\(M\)[/tex] 4 units to the right.
1. Identify the original coordinates of point [tex]\(M\)[/tex]:
- [tex]\(M(0, -1)\)[/tex]
2. Understand the translation rule:
- A translation of 4 units to the right changes the x-coordinate by adding 4 to it.
- The y-coordinate remains unchanged during the horizontal translation.
3. Apply the translation to the point [tex]\(M\)[/tex]:
- Calculate the new x-coordinate:
[tex]\[
M_{\text{x}}' = M_{\text{x}} + 4 = 0 + 4 = 4
\][/tex]
- Calculate the new y-coordinate (since it remains the same):
[tex]\[
M_{\text{y}}' = M_{\text{y}} = -1
\][/tex]
4. Construct the new coordinates of point [tex]\(M'\)[/tex]:
- [tex]\(M'(4, -1)\)[/tex]
Therefore, after translating point [tex]\(M\)[/tex] 4 units to the right, the new coordinates of [tex]\(M'\)[/tex] are [tex]\( (4, -1) \)[/tex].
Thus, the correct answer is:
[tex]\[ M^{\prime}(4, -1) \][/tex]
