Question

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

Explanation:

Step1: Find original coordinates

From the graph, \(A(-4, -1)\), \(B(-4, 4)\), \(C(3, 4)\), \(D(3, -1)\)

Step2: Apply dilation formula

For a dilation centered at the origin with scale factor \(k = 2\), the formula is \((x,y)\to(kx,ky)\)

• For \(A(-4, -1)\): \((-4\times2,-1\times2)=(-8,-2)\)
• For \(B(-4, 4)\): \((-4\times2,4\times2)=(-8,8)\)
• For \(C(3, 4)\): \((3\times2,4\times2)=(6,8)\)
• For \(D(3, -1)\): \((3\times2,-1\times2)=(6,-2)\)

Answer:

\(A'(-8,-2)\), \(B'(-8,8)\), \(C'(6,8)\), \(D'(6,-2)\)