Question

write the coordinates of the vertices after a dilation with a scale factor of 4, centered at the origin.

Explanation:

1. First, identify the original coordinates of the vertices:

• From the graph, the coordinates of point \(S\) are \((- 2,0)\), point \(P\) are \((1, - 1)\), point \(Q\) are \((2,-1)\), and point \(R\) are \((2,0)\).

1. Recall the rule for dilation centered at the origin:

• If a point \((x,y)\) is dilated with a scale - factor \(k\) centered at the origin, the new coordinates \((x',y')\) are given by \((x',y')=(k\cdot x,k\cdot y)\). Here, \(k = 4\).

1. Calculate the new coordinates for each vertex:

• For point \(S(-2,0)\):
• \(x'=4\times(-2)=-8\), \(y'=4\times0 = 0\). So the new coordinates of \(S\) are \((-8,0)\).
• For point \(P(1,-1)\):
• \(x'=4\times1 = 4\), \(y'=4\times(-1)=-4\). So the new coordinates of \(P\) are \((4,-4)\).
• For point \(Q(2,-1)\):
• \(x'=4\times2 = 8\), \(y'=4\times(-1)=-4\). So the new coordinates of \(Q\) are \((8,-4)\).
• For point \(R(2,0)\):
• \(x'=4\times2 = 8\), \(y'=4\times0 = 0\). So the new coordinates of \(R\) are \((8,0)\).

Step1: Identify original coordinates

Identified \(S(-2,0)\), \(P(1,-1)\), \(Q(2,-1)\), \(R(2,0)\)

Step2: Apply dilation formula

Used \((x',y')=(k\cdot x,k\cdot y)\) with \(k = 4\)

Step3: Calculate new coordinates for \(S\)

\(x'=4\times(-2)=-8\), \(y'=4\times0 = 0\)

Step4: Calculate new coordinates for \(P\)

\(x'=4\times1 = 4\), \(y'=4\times(-1)=-4\)

Step5: Calculate new coordinates for \(Q\)

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

Step6: Calculate new coordinates for \(R\)

\(x'=4\times2 = 8\), \(y'=4\times0 = 0\)

Answer:

The new coordinates of \(S\) are \((-8,0)\), of \(P\) are \((4,-4)\), of \(Q\) are \((8,-4)\), and of \(R\) are \((8,0)\)