Question

write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{3}$, centered at the origin.

Explanation:

Step1: Identify original coordinates

Assume $L(-9,- 9)$, $M(-9,9)$, $N(9,-9)$.

Step2: Apply dilation formula

For a dilation with scale - factor $k = \frac{1}{3}$ centered at the origin $(x,y)\to(kx,ky)$.
For point $L$: $x=-9,y = - 9$, new coordinates are $(\frac{1}{3}\times(-9),\frac{1}{3}\times(-9))=(-3,-3)$.
For point $M$: $x=-9,y = 9$, new coordinates are $(\frac{1}{3}\times(-9),\frac{1}{3}\times9)=(-3,3)$.
For point $N$: $x = 9,y=-9$, new coordinates are $(\frac{1}{3}\times9,\frac{1}{3}\times(-9))=(3,-3)$.

Answer:

The new coordinates of $L$ are $(-3,-3)$, of $M$ are $(-3,3)$, and of $N$ are $(3,-3)$.