Question

from unit 3, lesson 2
dilate quadrilateral abcd using center d and scale factor 2.

Explanation:

Step1: Locate points A, B, C relative to D

Since the center of dilation is D, we need to find the vectors from D to A, D to B, and D to C.

Step2: Apply dilation rule

For a dilation with scale factor \(k = 2\) and center \(D\), if a point \(P(x,y)\) (relative to center \(D\)) is dilated, the new point \(P'(x',y')\) is given by \(x'=2x\), \(y' = 2y\) (in vector - like terms, if \(\overrightarrow{DP}=(a,b)\), then \(\overrightarrow{DP'}=(2a,2b)\)).
For example, if we consider the distance and direction from \(D\) to \(A\), we double that distance and direction. Similarly for \(B\) and \(C\). Since \(D\) is the center of dilation, \(D\) remains in the same position.

Step3: Connect the dilated points

After finding the dilated positions of \(A\), \(B\), and \(C\) (let's call them \(A'\), \(B'\), \(C'\) with \(D'=D\)), we connect \(A'\) to \(B'\), \(B'\) to \(C'\), \(C'\) to \(D\), and \(D\) to \(A'\) to form the dilated quadrilateral.

Answer:

Construct the dilated quadrilateral by doubling the distance from \(D\) to \(A\), \(D\) to \(B\), and \(D\) to \(C\) (while keeping \(D\) fixed) and then connecting the new points.