Question

write the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.

Explanation:

Step1: Identify original coordinates

The original coordinates of the vertices are \(J(- 5,-5)\), \(K(3,-5)\), \(L(3,5)\), \(M(-5,5)\)

Step2: Apply dilation formula

For a dilation centered at the origin with scale - factor \(k = 2\), the formula to find the new coordinates \((x',y')\) of a point \((x,y)\) is \((x',y')=(k\cdot x,k\cdot y)\)
For point \(J(-5,-5)\):
\(x'=2\times(-5)=-10\), \(y'=2\times(-5)=-10\), so the new coordinates of \(J\) are \((-10,-10)\)
For point \(K(3,-5)\):
\(x'=2\times3 = 6\), \(y'=2\times(-5)=-10\), so the new coordinates of \(K\) are \((6,-10)\)
For point \(L(3,5)\):
\(x'=2\times3=6\), \(y'=2\times5 = 10\), so the new coordinates of \(L\) are \((6,10)\)
For point \(M(-5,5)\):
\(x'=2\times(-5)=-10\), \(y'=2\times5 = 10\), so the new coordinates of \(M\) are \((-10,10)\)

Answer:

The new coordinates of \(J\) are \((-10,-10)\), of \(K\) are \((6,-10)\), of \(L\) are \((6,10)\), of \(M\) are \((-10,10)\)