Question

1a: identify the vertices of this quadrilateral.1b: the quadrilateral is being dilated by a factor of 2. what are the new vertices of this quadrilateral? show all your work.

Explanation:

Step1: Recall the dilation formula

When a point \((x,y)\) is dilated by a factor \(k\) about the origin, the new point is \((kx,ky)\). Here \(k = 2\).

Step2: Apply the formula to each vertex

• For vertex \(A(2,1)\):

\(x = 2,y = 1,k=2\). New \(x\) - coordinate \(x'=2\times2 = 4\), new \(y\) - coordinate \(y'=2\times1=2\). So \(A'(4,2)\)

• For vertex \(B(2,4)\):

\(x = 2,y = 4,k = 2\). New \(x\) - coordinate \(x'=2\times2=4\), new \(y\) - coordinate \(y'=2\times4 = 8\). So \(B'(4,8)\)

• For vertex \(C(4,4)\):

\(x = 4,y = 4,k=2\). New \(x\) - coordinate \(x'=2\times4 = 8\), new \(y\) - coordinate \(y'=2\times4=8\). So \(C'(8,8)\)

• For vertex \(D(6,1)\):

\(x = 6,y = 1,k = 2\). New \(x\) - coordinate \(x'=2\times6=12\), new \(y\) - coordinate \(y'=2\times1 = 2\). So \(D'(12,2)\)

Answer:

The new vertices are \(A'(4,2)\), \(B'(4,8)\), \(C'(8,8)\), \(D'(12,2)\)