Question

write the coordinates of the vertices after a dilation with a scale factor of 3, centered at the origin.
j(□,□)
k(□,□)
l(□,□)
m(□,□)

Explanation:

Step1: Find the original coordinates

From the graph, the original coordinates are \(J(-3,-2)\), \(K(-1,-2)\), \(L(-1,2)\), \(M(-3,2)\).

Step2: Apply the dilation formula

The formula for dilation centered at the origin with scale factor \(k\) is \((x,y)\to(kx,ky)\). Here \(k = 3\).

• For \(J(-3,-2)\): \(J'=(3\times(-3),3\times(-2))=(-9,-6)\)
• For \(K(-1,-2)\): \(K'=(3\times(-1),3\times(-2))=(-3,-6)\)
• For \(L(-1,2)\): \(L'=(3\times(-1),3\times2)=(-3,6)\)
• For \(M(-3,2)\): \(M'=(3\times(-3),3\times2)=(-9,6)\)

Answer:

\(J'(-9,-6)\), \(K'(-3,-6)\), \(L'(-3,6)\), \(M'(-9,6)\)