Answer:
Center of dilation origin, The scale factor is 4, The dilation mapping is (x, y) → (4x,4y) and The image represents the shape of the triangle.
Step-by-step explanation:
Given Hector is making an art project by cutting and gluing fabric shapes to a wooden board. His design includes two similar triangles, with one 4 times the size of the other. He cuts the smaller fabric triangle and traces it onto grid paper. we have to tell how he can use the tracing to make a pattern for the larger fabric triangle.
Apply the center of dilation origin.
The scale factor is 4
The dilation mapping is (x, y) → (4x,4y)
The image represents the shape of the triangle.
The change as a percentage is 6.7 %
<h3>
How to calculate the percentage change ?</h3>
The price of the building in the year 2021 is $4,200,00
The price of the building in 2021 is $4,500,000
Therefore the percentage change can be calculated as follows
= 4,500,000 - 4,200,000/4,500,000 × 100
= 300,000/4,500,000 × 100
= 0.066 × 100
= 6.7 %
Hence the percentage change is 6.7%
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keeping in mind that the circle has a radius of 1.6 ft.
![\textit{area of a circle}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=1.6 \end{cases}\implies A=\pi (1.6)^2\implies A=2.56\pi \implies A\approx 8.04~ft^2 \\\\[-0.35em] ~\dotfill\\\\ \textit{circumference of a circle}\\\\ C=2\pi r~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=1.6 \end{cases}\implies C=2\pi (1.6)\implies C=3.2\pi \implies C\approx 10.05~ft](https://tex.z-dn.net/?f=%5Ctextit%7Barea%20of%20a%20circle%7D%5C%5C%5C%5C%20A%3D%5Cpi%20r%5E2%20~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D1.6%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Cpi%20%281.6%29%5E2%5Cimplies%20A%3D2.56%5Cpi%20%5Cimplies%20A%5Capprox%208.04~ft%5E2%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Ctextit%7Bcircumference%20of%20a%20circle%7D%5C%5C%5C%5C%20C%3D2%5Cpi%20r~~%20%5Cbegin%7Bcases%7D%20r%3Dradius%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20r%3D1.6%20%5Cend%7Bcases%7D%5Cimplies%20C%3D2%5Cpi%20%281.6%29%5Cimplies%20C%3D3.2%5Cpi%20%5Cimplies%20C%5Capprox%2010.05~ft)
Answer: y = 1/8x+1
y=mx+b is slope intercept form
given m = 1/8 and a point we can find b by plugging in what we have
1=1/8(8)+b
1=1b
b=1
So then we know m = 1/8 and b = 1
y=1/8x+1 is the answer
