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).
2 answers:
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
.... (1)
Distance formula:
Now, put these values in equation (1).
Therefore the scale factor of dilation is 2.
You might be interested in
You did not attach any picture to solve this problem. We cannot calculate for the value W’X’ without the correct illustrations. However, I think I found the correct one (see attached), please attach it next time.
So the first thing we have to do is to calculate for the dilation factor. Taking point G as the reference point, we can see that the distance of point G from rectangle W’X’Y’Z’ is 1.5 while the distance from rectangle WXYZ is (1.5 + 7.5), therefore the dilation factor to use is:
dilation factor = 1.5 / (1.5 + 7.5) = 1.5 / 9 = 1/6
Since WX has an initial measure of 3 units, therefore the measure of W’X’ is:
W’X’ = 3 units * (1/6) = 0.5 units
Answer:
<span>0.5 units</span>
