Question

write the coordinates of the vertices after a dilation with a scale factor of $\frac{1}{5}$, centered at the origin.
$c(\square,\square)$
$d(\square,\square)$
$e(\square,\square)$
$f(\square,\square)$

Explanation:

Step1: Find the original coordinates

From the graph, the coordinates are \(C(-10,-5)\), \(D(-10,0)\), \(E(0,-7)\), \(F(0,5)\).

Step2: Apply the dilation formula

For a dilation centered at the origin with scale factor \(k = \frac{1}{5}\), the formula is \((x,y)\to(kx,ky)\).

• For \(C(-10,-5)\):

\(x'=\frac{1}{5}\times(-10)=- 2\), \(y'=\frac{1}{5}\times(-5)=-1\). So \(C'(-2,-1)\).

• For \(D(-10,0)\):

\(x'=\frac{1}{5}\times(-10)=-2\), \(y'=\frac{1}{5}\times0 = 0\). So \(D'(-2,0)\).

• For \(E(0,-7)\):

\(x'=\frac{1}{5}\times0 = 0\), \(y'=\frac{1}{5}\times(-7)=-\frac{7}{5}=-1.4\). So \(E'(0,-1.4)\).

• For \(F(0,5)\):

\(x'=\frac{1}{5}\times0 = 0\), \(y'=\frac{1}{5}\times5 = 1\). So \(F'(0,1)\).

Answer:

\(C'(-2,-1)\), \(D'(-2,0)\), \(E'(0,-1.4)\), \(F'(0,1)\)