Answer:
The image of R=(4,-2) for a dilation with center (0, 0) and a scale factor of 1 1/2 is: First option (6,-3)
Step-by-step explanation:
The image of a point P=(x,y) for a dilation with center at the origin O=(0, 0) and a scale factor of f is: P'=(f*x,f*y).
In this case the point is R=(4,-2)=(x,y)→x=4, y=-2
And the scale factor is:
[tex]f=1\frac{1}{2}=\frac{1(2)+1}{2}=\frac{2+1}{2}\\ f=\frac{3}{2}[/tex]
Then the image of point R=(4,-2) for a dilation with center at the origin O=(0,0) and a scale factor of f=1 1/2=3/2 is:
[tex]R'=(f.x,f.y)\\ R'=(\frac{3}{2}(4),\frac{3}{2}(-2))\\ R'=(\frac{3(4)}{2},\frac{3(-2)}{2})\\ R'=(\frac{12}{2},\frac{-6}{2} )[/tex]
R'=(6,-3)
