Question

draw the image of rectangle abcd under dilation using center p and scale factor 1/2

Explanation:

Step1: Connect center P to vertices

Draw lines from center \(P\) to vertices \(A\), \(B\), \(C\), and \(D\) of rectangle \(ABCD\).

Step2: Measure distances and scale

Measure the distance from \(P\) to each vertex. Multiply each distance by the scale - factor \(\frac{1}{3}\) to find the new points. For example, if the distance from \(P\) to \(A\) is \(d_{PA}\), the new distance from \(P\) to \(A'\) (the image of \(A\)) is \(d_{PA'}=\frac{1}{3}d_{PA}\).

Step3: Locate new vertices

Locate the new vertices \(A'\), \(B'\), \(C'\), and \(D'\) along the lines drawn in Step 1 at the scaled - distances.

Step4: Draw the new rectangle

Connect the new vertices \(A'\), \(B'\), \(C'\), and \(D'\) in order to form the dilated rectangle.

Answer:

A new rectangle \(A'B'C'D'\) is drawn with vertices located by dilating the vertices of rectangle \(ABCD\) with center \(P\) and scale - factor \(\frac{1}{3}\). (Since this is a drawing problem, the actual visual drawing cannot be provided in text form, but the steps to create it are given).