Question

write the coordinates of the vertices after a dilation with a scale factor of 4, centered at the origin.

Explanation:

Step1: Identify original coordinates

The original coordinates of \(L\) are \((- 2,-2)\), of \(M\) are \((-2,2)\) and of \(N\) are \((0, - 2)\).

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k\), the formula to find the new coordinates \((x',y')\) of a point \((x,y)\) is \((x',y')=(k\times x,k\times y)\). Here \(k = 4\).
For point \(L(-2,-2)\):
\(x'=4\times(-2)=-8\), \(y'=4\times(-2)=-8\), so \(L'(-8,-8)\).
For point \(M(-2,2)\):
\(x'=4\times(-2)=-8\), \(y'=4\times2 = 8\), so \(M'(-8,8)\).
For point \(N(0,-2)\):
\(x'=4\times0 = 0\), \(y'=4\times(-2)=-8\), so \(N'(0,-8)\).

Answer:

\(L'(-8,-8)\), \(M'(-8,8)\), \(N'(0,-8)\)