Question

answer the following questions. make sure to explain all your work and show all your steps.

1. analyze the following quadrilateral.

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 scale factor \(k\) with the origin as the center of dilation, 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 \(=2\times2=4\), new \(y\) - coordinate \(=1\times2 = 2\). So \(A'(4,2)\)

• For vertex \(B(2,4)\):

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

• For vertex \(C(3,4)\):

\(x = 3,y = 4,k=2\). New \(x\) - coordinate \(=3\times2 = 6\), new \(y\) - coordinate \(=4\times2=8\). So \(C'(6,8)\)

• For vertex \(D(6,1)\):

\(x=6,y = 1,k = 2\). New \(x\) - coordinate \(=6\times2=12\), new \(y\) - coordinate \(=1\times2=2\). So \(D'(12,2)\)

Answer:

The new vertices of the dilated quadrilateral are \(A'(4,2)\), \(B'(4,8)\), \(C'(6,8)\) and \(D'(12,2)\)