Question

1. square defg with vertices d(0, 0), e(2, 4), f(6, 2), and g(4, -2): k = 5/2
2. triangle stu with vertices s(-15, -3), t(-12, -15), and u(0, -9): k = 1/3

d: f: s: u:
e: g: t:

Explanation:

Step1: Calculate coordinates for square DEFG

For a dilation with scale factor \(k\), if a point \((x,y)\) is dilated, the new point \((x',y')=(kx,ky)\)

• For \(D(0,0)\): \(D'=( \frac{5}{2}\times0,\frac{5}{2}\times0)=(0,0)\)
• For \(E(2,4)\): \(E'=( \frac{5}{2}\times2,\frac{5}{2}\times4)=(5,10)\)
• For \(F(6,2)\): \(F'=( \frac{5}{2}\times6,\frac{5}{2}\times2)=(15,5)\)
• For \(G(4, - 2)\): \(G'=( \frac{5}{2}\times4,\frac{5}{2}\times(-2))=(10,-5)\)

Step2: Calculate coordinates for triangle STU

• For \(S(-15,-3)\): \(S'=( \frac{1}{3}\times(-15),\frac{1}{3}\times(-3))=(-5,-1)\)
• For \(T(-12,-15)\): \(T'=( \frac{1}{3}\times(-12),\frac{1}{3}\times(-15))=(-4,-5)\)
• For \(U(0,-9)\): \(U'=( \frac{1}{3}\times0,\frac{1}{3}\times(-9))=(0,-3)\)

Answer:

\(E'\): \((5,10)\)	\(G'\): \((10,-5)\)	\(T'\): \((-4,-5)\)