1) A \(12\)-inch by \(15\)-inch print is reduced by a scale factor of \(\Large\frac{5}{6}\). What are the dimensions of the new photograph? Compare the areas of the pre-image and image.
2) The vertices of \(\triangle{DOG}\) are \(D(1, 8)\), \(O (7, 3)\) and \(G (8, 0)\). Find the vertices of the image after the dilation described:
a) Dilate \(\triangle{DOG}\) using center \((8, 0)\) with a scale factor of \(3\).
b) Dilate \(\triangle{DOG}\) using center \((3, 3)\) with a scale factor of \(4\).
c) Dilate \(\triangle{DOG}\) using center \((-1, 12)\) with a scale factor of \(0.5\).
d) Dilate \(\triangle{DOG}\) using center \((-1, -1)\) with a scale factor of \(\Large\frac{2}{3}\).
2) The vertices of \(\triangle{DOG}\) are \(D(1, 8)\), \(O (7, 3)\) and \(G (8, 0)\). Find the vertices of the image after the dilation described:
a) Dilate \(\triangle{DOG}\) using center \((8, 0)\) with a scale factor of \(3\).
b) Dilate \(\triangle{DOG}\) using center \((3, 3)\) with a scale factor of \(4\).
c) Dilate \(\triangle{DOG}\) using center \((-1, 12)\) with a scale factor of \(0.5\).
d) Dilate \(\triangle{DOG}\) using center \((-1, -1)\) with a scale factor of \(\Large\frac{2}{3}\).
5) Given \(CATS\) sketch the image using point \(P\) for the center of dilation, graph the dilations based on the scale factor.
a) \(k = -3\)
b) \(k = -\Large\frac{1}{2}\)
c) \(k = -1\)
a) \(k = -3\)
b) \(k = -\Large\frac{1}{2}\)
c) \(k = -1\)
6) Consider how you would explain to another student who had missed our lessons on dilation transformations and needed to know the steps for determining a dilation given any center of dilation and any scale factor. You may use an illustration to assist your explanation but your steps should be applicable for any dilation.
7) Derive the coordinate rule for dilating a point with the center of the dilation not at the origin \((a, b)\) and scale factor \(k\).
Solution Bank