write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{5}$, centered at the…

Explanation:

Step1: Identify original coordinates

The original coordinates of the vertices are (A(5,0)), (B(5,10)), (C(- 5,0)).

Step2: Apply dilation formula

For a dilation with scale - factor (k=\frac{1}{5}) centered at the origin ((x,y)\to(kx,ky)). For point (A(5,0)): (x = 5,y = 0,k=\frac{1}{5}), then the new coordinates are ((\frac{1}{5}\times5,\frac{1}{5}\times0)=(1,0)). For point (B(5,10)): (x = 5,y = 10,k=\frac{1}{5}), then the new coordinates are ((\frac{1}{5}\times5,\frac{1}{5}\times10)=(1,2)). For point (C(-5,0)): (x=-5,y = 0,k=\frac{1}{5}), then the new coordinates are ((\frac{1}{5}\times(-5),\frac{1}{5}\times0)=(-1,0)).

Answer:

The new coordinates of (A) are ((1,0)), of (B) are ((1,2)) and of (C) are ((-1,0))