write the coordinates of the vertices after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Identify original coordinates

$B(-1,-1), C(-1,1), D(1,1), E(1,-1)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k$, the formula is $(x,y)\to(kx,ky)$. Here $k = 4$. For point $B$: $x=-1,y = - 1$, new coordinates are $(4\times(-1),4\times(-1))=(-4,-4)$. For point $C$: $x=-1,y = 1$, new coordinates are $(4\times(-1),4\times1)=(-4,4)$. For point $D$: $x = 1,y = 1$, new coordinates are $(4\times1,4\times1)=(4,4)$. For point $E$: $x = 1,y=-1$, new coordinates are $(4\times1,4\times(-1))=(4,-4)$.

Answer:

$B'(-4,-4),C'(-4,4),D'(4,4),E'(4,-4)$