The correct option is [tex]\boxed{\bf option C}[/tex] i.e., [tex]\boxed{\bf (-6,-3)}[/tex].
Further Explanation:
Given:
There is a rectangle DEFG on a cartesian plane and the points are [tex]\text{D}(-2,-1)[/tex], [tex]\text{E}(-2,1)[/tex], [tex]\text{F}(2,1)[/tex] and [tex]\text{G}(2,-1)[/tex].
The objective is to find the coordinates of the point D when it is dilated by the factor of [tex]3[/tex] with dilated center of [tex](0,0)[/tex].
Dilation means it is a transformation which produces images which is having same shape as original but it is of different size.
The description of dilation includes scaling factor and dilation center.
As we know dilating the figure by the scale factor of [tex]k[/tex] then we will multiply the coordinates of all points of the figure by the scaling factor [tex]k[/tex] such that,
[tex]\boxed{(x,y)\rightarrow(kx,ky)\text{ (after dialation)}}[/tex]
It can be seen that the coordinates of point D are [tex](-2,-1)[/tex] and after dilation by the scale factor of [tex]3[/tex], the coordinates of D gives D' and it can be written as follows:
[tex]\boxed{\left((-2\cdot 3),(-1\cdot 3)\right)\rightarrow(-6,-3)}[/tex]
Therefore the coordinates of point D after dilation will be [tex](-6,-3)[/tex] and can be seen in figure 1 (attached in the end).
Thus, the correct option is [tex]\boxed{\bf option C}[/tex] i.e., [tex]\boxed{\bf (-6,-3)}[/tex].
Learn more
1. Learn more about the coordinates of triangles after rotation https://brainly.com/question/7437053
2. Learn more about the transformation of the triangle when rotated about origin https://brainly.com/question/2992432
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Coordinate geometry
Keywords: Rectangle DEFG, coordinate points, dilation, scaling factor, center, multiplication, coordinate geometry, shifting, graph, dilated center, transformation, shifting, geometry, coordinate.
