Question

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

Explanation:

Step1: Identify original coordinates

$M(0,0)$, $N(-2, - 1)$, $K(-1,-2)$, $L(2, - 1)$

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor $k = 4$, the formula is $(x,y)\to(kx,ky)$.
For point $M$: $(0,0)\to(4\times0,4\times0)=(0,0)$
For point $N$: $(-2,-1)\to(4\times(-2),4\times(-1))=(-8,-4)$
For point $K$: $(-1,-2)\to(4\times(-1),4\times(-2))=(-4,-8)$
For point $L$: $(2,-1)\to(4\times2,4\times(-1))=(8,-4)$

Answer:

$M'(0,0)$, $N'(-8,-4)$, $K'(-4,-8)$, $L'(8,-4)$