Question

write the coordinates of the vertices after a dilation with a scale factor of 4, centered at the origin.
q( )
r( )
s( )
t( )

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin with scale - factor \(k\), if a point has coordinates \((x,y)\), the new coordinates \((x',y')\) after dilation are given by \((x',y')=(k\cdot x,k\cdot y)\). Here \(k = 4\).

Step2: Find coordinates of point \(Q\)

The original coordinates of \(Q\) are \((- 1,-2)\). Using the dilation formula, \(x'=4\times(-1)=-4\) and \(y'=4\times(-2)=-8\). So \(Q'(-4,-8)\).

Step3: Find coordinates of point \(R\)

The original coordinates of \(R\) are \((1,-2)\). Then \(x'=4\times1 = 4\) and \(y'=4\times(-2)=-8\). So \(R'(4,-8)\).

Step4: Find coordinates of point \(S\)

The original coordinates of \(S\) are \((1,0)\). Then \(x'=4\times1 = 4\) and \(y'=4\times0 = 0\). So \(S'(4,0)\).

Step5: Find coordinates of point \(T\)

The original coordinates of \(T\) are \((-1,0)\). Then \(x'=4\times(-1)=-4\) and \(y'=4\times0 = 0\). So \(T'(-4,0)\).

Answer:

\(Q(-4,-8)\)
\(R(4,-8)\)
\(S(4,0)\)
\(T(-4,0)\)