Question

10 what is the center of dilation and the scale factor of quadrilateral abcd? center = scale factor =

Explanation:

Step1: Identify the center of dilation

The center of dilation is the point that remains fixed during the dilation. Looking at the graph, we can observe that the point \((0,6)\) is the fixed point.

Step2: Calculate the scale factor

Let's consider a point \(A\) and its image \(A'\). Suppose the distance from the center of dilation to \(A\) is \(d_1\) and to \(A'\) is \(d_2\).
If we assume the center of dilation \(O=(0,6)\), for a vertical segment:
Let's say the \(y -\) coordinate of \(A\) is \(3\) and of \(A'\) is \(6\). The distance from \(O\) to \(A\) (vertical) is \(|6 - 3|=3\), and from \(O\) to \(A'\) (vertical) is \(|6 - 6| = 0\) (incorrect approach). Let's use horizontal distance.
Suppose a horizontal segment: assume a point \(A\) (say \(x\) - coordinate of \(A\) is \( - 2\), \(y\) - coordinate \(3\)) and \(A'\) (\(x\) - coordinate \(-6\), \(y\) - coordinate \(6\)). The distance from the center \((0,6)\) to \(A\) (horizontal) is \(|0-(- 2)| = 2\), and from the center \((0,6)\) to \(A'\) (horizontal) is \(|0-(-6)|=6\).
The scale factor \(k=\frac{\text{distance from center to }A'}{\text{distance from center to }A}\)
\(k = 3\)

Answer:

Center \(=(0,6)\)
Scale factor \(=3\)