Answer:
B'(16,14)
Step-by-step explanation:
First find the coordinates of the vertex B. The center of the square M is the midpoint of the diagonal AC. Since A(2,7) and C(8,1), the center has coordinates
[tex]M\left(\dfrac{2+8}{2},\dfrac{7+1}{2}\right)=M(5,4).[/tex]
Point M is also the midpoint of the diagonal BD. Let B has coordinates (x,y), then
[tex]\dfrac{x+2}{2}=5\Rightarrow x=8,\\ \\\dfrac{y+1}{2}=4\Rightarrow y=7.[/tex]
Hence, B(8,7).
Now, the dilation by a scale factor 2 with the center of dilation at the origin has the rule
(x,y)→(2x,2y).
Thus,
B(8,7)→B'(16,14).
