To find the image of a point under a dilation centered at [tex]\((0,0)\)[/tex], you multiply each coordinate of the point by the scale factor [tex]\(D\)[/tex]. Given that the point [tex]\(P(-3, 5)\)[/tex] and the scale factor [tex]\(D_1\)[/tex] are provided:
1. Identify the coordinates of point [tex]\(P\)[/tex]: [tex]\((-3, 5)\)[/tex].
2. Determine the scale factor [tex]\(D_1\)[/tex]. In this case, [tex]\(D_1\)[/tex] appears to result in the original point itself, signifying an identity transformation, which has a scale factor of 1.
3. Apply the dilation transformation by multiplying each coordinate of [tex]\(P\)[/tex] by the scale factor:
[tex]\[
x' = D_1 \cdot x = 1 \cdot (-3) = -3
\][/tex]
[tex]\[
y' = D_1 \cdot y = 1 \cdot 5 = 5
\][/tex]
So, the image of the point [tex]\((-3, 5)\)[/tex] after dilation by the scale factor [tex]\(D_1\)[/tex] is [tex]\((-3, 5)\)[/tex].
Amongst the given options:
A. [tex]\((5, -3)\)[/tex]
B. [tex]\((6, -2)\)[/tex]
C. [tex]\((-3, 5)\)[/tex]
The correct answer is:
C. [tex]\((-3, 5)\)[/tex]
