Question

write the coordinates of the vertices after a dilation with a scale factor of 2, centered at the origin.
q((
r(
s(

Explanation:

Step1: Find the original coordinates

From the graph, the coordinates are \(Q(-3,-4)\), \(R(-1,-4)\), \(S(0,5)\).

Step2: Apply the dilation formula

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

• For \(Q(-3,-4)\): \(Q'=(2\times(-3),2\times(-4))=(-6,-8)\)
• For \(R(-1,-4)\): \(R'=(2\times(-1),2\times(-4))=(-2,-8)\)
• For \(S(0,5)\): \(S'=(2\times0,2\times5)=(0,10)\)

Answer:

\(Q'(-6,-8)\), \(R'(-2,-8)\), \(S'(0,10)\)