Pre-image ABCD is dilated to be image A′B′C′D′ . The origin is the center of dilation. What scale factor is used to create the dilation? Enter your answer in the box. Two rectangles on a coordinate plane. rectangle ABCD has vertices a at (1, 4), b at (3, 4), c at (3, 1), and d at (1, 1). rectangle A prime b prime c prime d prime has coordinates a prime at (2, 8), b prime at (6, 8), c prime at (6, 2) and d prime at (2, 2).
Accepted Solution
A:
Answer:The scale factor of dilation is 2.Step-by-step explanation:From the given information it is notices that the vertices of preimage are A(1, 4), B(3, 4), C(3, 1), and D(1, 1). The vertices of image are A'(2, 8), B'(6, 8), C'(6, 2) and D'(2, 2).The scale factor is the ratio of distance of a image of a vertex from the center of dilation and distance of the vertex from the center of dilation.The center of dilation is origin. So, the scale factor is[tex]k=\frac{OA'}{OA}[/tex] .... (1)Distance formula:[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex]OA'=\sqrt{(2-0)^2+(8-0)^2}=\sqrt{4+64}=\sqrt{68}=2\sqrt{17}[/tex][tex]OA=\sqrt{(1-0)^2+(4-0)^2}=\sqrt{1+16}=\sqrt{17}[/tex]Now, put these values in equation (1).[tex]k=\frac{2\sqrt{17}}{\sqrt{17}}[/tex][tex]k=2[/tex]Therefore the scale factor of dilation is 2.