Question

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

$q (\square, \square)$
$r (\square, \square)$
$s (\square, \square)$

Explanation:

Step1: Find original coordinates

From the graph, \(Q(10,-10)\), \(R(10,5)\), \(S(0,-10)\)

Step2: Apply 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 \(Q(10,-10)\):

\(x'=\frac{1}{5}\times10 = 2\), \(y'=\frac{1}{5}\times(-10)=-2\), so \(Q'(2,-2)\)

• For \(R(10,5)\):

\(x'=\frac{1}{5}\times10 = 2\), \(y'=\frac{1}{5}\times5 = 1\), so \(R'(2,1)\)

• For \(S(0,-10)\):

\(x'=\frac{1}{5}\times0 = 0\), \(y'=\frac{1}{5}\times(-10)=-2\), so \(S'(0,-2)\)

Answer:

\(Q'(2,-2)\), \(R'(2,1)\), \(S'(0,-2)\)