Question

write the coordinates of the vertices after a dilation with a scale factor of 4, centered at the origin. video p ( ) q ( ) r ( ) s ( ) submit

Explanation:

Step1: Find the original coordinates

The original coordinates are \(P(-2,-1)\), \(Q(-2,2)\), \(R(2,2)\), \(S(2,-1)\).

Step2: Apply the dilation formula

For a dilation centered at the origin with scale factor \(k = 4\), the formula is \((x,y)\to(kx,ky)\).

• For \(P(-2,-1)\):

\(P'=(4\times(-2),4\times(-1))=(-8,-4)\)

• For \(Q(-2,2)\):

\(Q'=(4\times(-2),4\times2)=(-8,8)\)

• For \(R(2,2)\):

\(R'=(4\times2,4\times2)=(8,8)\)

• For \(S(2,-1)\):

\(S'=(4\times2,4\times(-1))=(8,-4)\)

Answer:

\(P'(-8,-4)\), \(Q'(-8,8)\), \(R'(8,8)\), \(S'(8,-4)\)