Question

write the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.
r(□,□)
u(□,□)
v(□,□)
w(□,□)

Explanation:

Step1: Find original coordinates

Original coordinates: \( r(-4,-4) \), \( u(-4,-2) \), \( v(-2,-2) \), \( w(-2,-4) \)

Step2: Apply dilation formula

Dilation formula: \((x,y)\to(2x,2y)\) (scale factor \(k = 2\) centered at origin)

• For \(r(-4,-4)\): \( (2\times(-4),2\times(-4))=(-8,-8) \)
• For \(u(-4,-2)\): \( (2\times(-4),2\times(-2))=(-8,-4) \)
• For \(v(-2,-2)\): \( (2\times(-2),2\times(-2))=(-4,-4) \)
• For \(w(-2,-4)\): \( (2\times(-2),2\times(-4))=(-4,-8) \)

Answer:

\( r(-8,-8) \), \( u(-8,-4) \), \( v(-4,-4) \), \( w(-4,-8) \)