Question

1. dilate abcd by a scale factor of 2. pre - image a(-2,-1) b(-2,2) c(1,2) d(1,-1) image algebraic rule: 2. dilate efg by a scale factor of 3/2. pre - image e(3,1) f(3,3) g(6,3) image algebraic rule:

Explanation:

Step1: Recall dilation rule

For a dilation with scale - factor \(k\) centered at the origin, the algebraic rule is \((x,y)\to(kx,ky)\). Here \(k = 2\).

Step2: Find coordinates of dilated points for rectangle \(ABCD\)

Point \(A(- 4,-2)\): \((-4,-2)\to(2\times(-4),2\times(-2))=(-8,-4)\)
Point \(B(-4,2)\): \((-4,2)\to(2\times(-4),2\times2)=(-8,4)\)
Point \(C(1,2)\): \((1,2)\to(2\times1,2\times2)=(2,4)\)
Point \(D(1,-2)\): \((1,-2)\to(2\times1,2\times(-2))=(2,-4)\)

Step3: Find coordinates of dilated points for triangle \(EFG\)

Point \(E(3,3)\): \((3,3)\to(2\times3,2\times3)=(6,6)\)
Point \(F(1,3)\): \((1,3)\to(2\times1,2\times3)=(2,6)\)
Point \(G(3,9)\): \((3,9)\to(2\times3,2\times9)=(6,18)\)

Answer:

For rectangle \(ABCD\):
Pre - image: \(A(-4,-2)\), \(B(-4,2)\), \(C(1,2)\), \(D(1,-2)\)
Image: \(A'(-8,-4)\), \(B'(-8,4)\), \(C'(2,4)\), \(D'(2,-4)\)
Algebraic rule: \((x,y)\to(2x,2y)\)

For triangle \(EFG\):
Pre - image: \(E(3,3)\), \(F(1,3)\), \(G(3,9)\)
Image: \(E'(6,6)\), \(F'(2,6)\), \(G'(6,18)\)
Algebraic rule: \((x,y)\to(2x,2y)\)