Question

activity 2: dilations on a grid
example 1:
find the dilation of quadrilateral abcd with center p and scale factor 2.
draw the new shape on the grid.

Explanation:

Step1: Understand Dilation

Dilation is a transformation that enlarges or reduces a figure. Here, the scale factor is \(2\), so each vertex of quadrilateral \(ABCD\) will be moved twice as far from the center \(P\).

Step2: Find New Coordinates (assuming grid - based movement from \(P\))

Let's assume we can count grid units from \(P\) to each vertex (\(A\), \(B\), \(C\), \(D\)). For example, if from \(P\) to \(A\) is \(x\) units right and \(y\) units up, then the new \(A'\) (dilated \(A\)) will be \(2x\) units right and \(2y\) units up from \(P\). Do the same for \(B\), \(C\), and \(D\).

Step3: Plot New Vertices

After calculating the new positions of \(A'\), \(B'\), \(C'\), \(D'\) (based on double the distance from \(P\) as the original vertices), connect these new vertices to form the dilated quadrilateral.

Answer:

Please refer to the above steps to draw the dilated quadrilateral on the grid by first determining the new positions of vertices \(A\), \(B\), \(C\), \(D\) (doubling their distance from center \(P\)) and then connecting them.