Question

find the new coordinates of this triangle after being dilated by a scale factor of 5 about the origin. preimage d(1,-1) e(1,2) f(-2,0) image d____ e__ f__ write the algebraic description here:____

Explanation:

Step1: Multiply coordinates by scale factor

For a dilation about the origin with scale factor \(k = 5\), the rule is \((x,y)\to(kx,ky)\).
For point \(D(1,-1)\):
\(D'\) has coordinates \((5\times1,5\times(-1))=(5,-5)\)

Step2: Apply dilation to \(E\)

For point \(E(1,2)\):
\(E'\) has coordinates \((5\times1,5\times2)=(5,10)\)

Step3: Apply dilation to \(F\)

For point \(F(-2,0)\):
\(F'\) has coordinates \((5\times(-2),5\times0)=(-10,0)\)

Answer:

\(D'(5,-5)\)
\(E'(5,10)\)
\(F'(-10,0)\)
Algebraic description: \((x,y)\to(5x,5y)\)