Answer:the answer is 7
Step-by-step explanation:
<u>Answer:</u>
3/4
<u>Step-by-step explanation:</u>
We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(−5, −4), B(−7, 3) and C(3, −2) to the image triangle A'B'C' with vertices A' (−3.75, −3), B' (−5.25, 2.25) and C' (2.25, −1.5).
Center of dilation is at the origin.
To find the scale factor, we will divide the corresponding vertices of the image and pre-image.
A(−5, −4) ---> A' (−3.75, −3) = ![\frac{-3.75}{-5} , \frac{-3}{-4}=(\frac{3}{4} , \frac{3}{4})](https://tex.z-dn.net/?f=%5Cfrac%7B-3.75%7D%7B-5%7D%20%2C%20%5Cfrac%7B-3%7D%7B-4%7D%3D%28%5Cfrac%7B3%7D%7B4%7D%20%2C%20%5Cfrac%7B3%7D%7B4%7D%29)
B(−7, 3) ---> B' (−5.25, 2.25) = ![\frac{-5.25}{-7} , \frac{2.25}{3}=(\frac{3}{4} , \frac{3}{4})](https://tex.z-dn.net/?f=%5Cfrac%7B-5.25%7D%7B-7%7D%20%2C%20%5Cfrac%7B2.25%7D%7B3%7D%3D%28%5Cfrac%7B3%7D%7B4%7D%20%2C%20%5Cfrac%7B3%7D%7B4%7D%29)
C(3, −2) ---> C' (2.25, −1.5) = ![\frac{2.25}{3} , \frac{-1.5}{-2}=(\frac{3}{4} , \frac{3}{4})](https://tex.z-dn.net/?f=%5Cfrac%7B2.25%7D%7B3%7D%20%2C%20%5Cfrac%7B-1.5%7D%7B-2%7D%3D%28%5Cfrac%7B3%7D%7B4%7D%20%2C%20%5Cfrac%7B3%7D%7B4%7D%29)
Therefore, the scale factor of the dilation is 3/4.
Letter B would be the answer.
2L + 2(1/2L) = 90
2L + L = 90
3L = 90
L = 30
(1/2)(30) = 15
W = 15
CHECK:
30 + 30 + 15 + 15 = 90
Area of the shaded region = area of sector ACE - area of Sector ABD
Area of sector ACE = 45/360 * 3.14(7)^2 = 19.2325 square units
Area of sector ABD = 45/360 * 3.14(5)^2 = 9.8125
Area of the shaded region = area of sector ACE - area of Sector ABD = 19.2325 - 9.8125 = 9.42 square units.