1. What is the scale factor for the dilation shown?
2. ΔRST has vertices R(0,0), S(4,2), and T(2,−2). ΔR′S′T′ is the image of ΔRST after a dilation with center (0,0) and scale factor 1 half . What are the coordinates of point S′?
3. The coordinates of ΔLMN are L(1,3), M(3,7), and N(5,5). Draw a graph showing ΔLMN and the image of ΔLMN for the dilation with center (0,0) and scale factor 1 half .
4. Writing ΔKLM has vertices K(1,3), L(3,7), and M(7,5). Draw a graph showing ΔKLM and ΔK′L′M′, its image after a dilation with center K and scale factor 2.
5. Reasoning Draw a graph showing ΔD′E′F′, the image of ΔDEF after a dilation.
6. Error Analysis For the dilation with center (0,0) shown on the graph, your friend says the scale factor is 7 halves .
a. What is the correct scale factor?
b. What mistake did your friend likely make?
A. Your friend found the ratio between two sides of the original triangle.
B. Your friend found the ratio between two sides of the image triangle.
C. Your friend found the scale factor that enlarges ΔA′B′C′ to ΔABC.
D. Your friend found the ratio between non-corresponding sides.
7. Photography A photographer uses a computer program to enlarge a photograph. When laid on a grid, the original photograph has coordinates P(0,0), H(12,0), O(12,8), and T(0,8). Draw a graph showing rectangles PHOT and P′H′O′T′, its image after a dilation with center at the origin and scale factor 11 over 4 .
8. Rectangle QUAD has coordinates Q(5,4), U(5,8), A(10,8), and D(10,4). Q′U′A′D′ is the image of QUAD after a dilation with center (0,0) and scale factor 2. What are the coordinates of point D′?