Answer: [tex](-10,-5)[/tex]
Step-by-step explanation:
I assume that you need the new coordinates of the point after Dilation centered at the origin.
For this exercise it is important to remember the definition of "Dilation".
Dilation is defined as a transformation in whicih the Image obtained after the transformation, has the same shape as the Pre-image, but its size is different.
Given a point [tex](x,y)[/tex] and a scale factor [tex]k[/tex], the new point after Dilation would be:
[tex](k*x,k*y)[/tex]
In this case, knowing that the original point is:
[tex](-4,-2)[/tex]
And the scale factor is the following:
[tex]k=\frac{5}{2}[/tex]
You need to multiply the x-coordinate and the y-coordinate of the original point by the scale factor given in the exercise, in order to find the coordinates of the new point.
Applying this procedure, you get that this is:
[tex]=((-4)(\frac{5}{2}),(-2)(\frac{5}{2}))=(-10,-5)[/tex]
