To determine the new coordinates when the point [tex]\((-3, 5)\)[/tex] is shifted 4 units to the right and 3 units down, follow these steps:
1. Horizontal Shift:
- Shifting a point to the right means adding to the [tex]\(x\)[/tex]-coordinate.
- The original [tex]\(x\)[/tex]-coordinate is [tex]\(-3\)[/tex].
- Adding 4 units to [tex]\(-3\)[/tex] gives:
[tex]\[
-3 + 4 = 1
\][/tex]
2. Vertical Shift:
- Shifting a point downward means subtracting from the [tex]\(y\)[/tex]-coordinate.
- The original [tex]\(y\)[/tex]-coordinate is [tex]\(5\)[/tex].
- Subtracting 3 units from [tex]\(5\)[/tex] gives:
[tex]\[
5 - 3 = 2
\][/tex]
Thus, the new coordinates of the point after the transformation are [tex]\((1, 2)\)[/tex].
Therefore, the correct answer is:
D [tex]\((1, 2)\)[/tex]
