Question

write the coordinates of the vertices after a dilation with a scale factor of 3, centered at the origin.

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 \(k = 3\).

Step2: Find coordinates of point \(B\)

The coordinates of point \(B\) are \((- 2,-2)\). Using the dilation formula, \(x'=3\times(-2)=-6\) and \(y'=3\times(-2)=-6\). So \(B'(-6,-6)\).

Step3: Find coordinates of point \(C\)

The coordinates of point \(C\) are \((2,-2)\). Using the dilation formula, \(x'=3\times2 = 6\) and \(y'=3\times(-2)=-6\). So \(C'(6,-6)\).

Step4: Find coordinates of point \(D\)

The coordinates of point \(D\) are \((2,2)\). Using the dilation formula, \(x'=3\times2 = 6\) and \(y'=3\times2=6\). So \(D'(6,6)\).

Step5: Find coordinates of point \(E\)

The coordinates of point \(E\) are \((-2,2)\). Using the dilation formula, \(x'=3\times(-2)=-6\) and \(y'=3\times2 = 6\). So \(E'(-6,6)\).

Answer:

\(B'(-6,-6)\)
\(C'(6,-6)\)
\(D'(6,6)\)
\(E'(-6,6)\)