Answer:
![2\sqrt {2}](https://tex.z-dn.net/?f=2%5Csqrt%20%7B2%7D)
Step-by-step explanation:
<u>Distance From a Point to a Line</u>
Given a line with an equation
:
ax + by + c = 0
And the point ![(x_0,y_0)](https://tex.z-dn.net/?f=%28x_0%2Cy_0%29)
The distance from the line to the point is given by
![\displaystyle d=\frac {|ax_{0}+by_{0}+c|}{\sqrt {a^{2}+b^{2}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%3D%5Cfrac%20%7B%7Cax_%7B0%7D%2Bby_%7B0%7D%2Bc%7C%7D%7B%5Csqrt%20%7Ba%5E%7B2%7D%2Bb%5E%7B2%7D%7D%7D)
The triangle has a vertex at (1,-2) and the base lies on the equation
x + y = 3
Rearranging:
x + y - 3 = 0
The altitude of the triangle is the distance from the point to the line.
The values to use in the formula of the distance are: a=1, b=1, c=-3, xo=1, yo=-2:
![\displaystyle d=\frac {|1*1+1*(-2)-3|}{\sqrt {1^{2}+1^{2}}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%3D%5Cfrac%20%7B%7C1%2A1%2B1%2A%28-2%29-3%7C%7D%7B%5Csqrt%20%7B1%5E%7B2%7D%2B1%5E%7B2%7D%7D%7D)
![\displaystyle d=\frac {|1-2-3|}{\sqrt {2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%3D%5Cfrac%20%7B%7C1-2-3%7C%7D%7B%5Csqrt%20%7B2%7D%7D)
![\displaystyle d=\frac {4}{\sqrt {2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%3D%5Cfrac%20%7B4%7D%7B%5Csqrt%20%7B2%7D%7D)
Rationalizing:
![\displaystyle d=\frac {4}{\sqrt {2}}\cdot\frac{\sqrt {2}}{\sqrt {2}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%3D%5Cfrac%20%7B4%7D%7B%5Csqrt%20%7B2%7D%7D%5Ccdot%5Cfrac%7B%5Csqrt%20%7B2%7D%7D%7B%5Csqrt%20%7B2%7D%7D)
![\displaystyle d=2\sqrt {2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20d%3D2%5Csqrt%20%7B2%7D)
The altitude of the triangle is ![\mathbf{4\sqrt {2}}](https://tex.z-dn.net/?f=%5Cmathbf%7B4%5Csqrt%20%7B2%7D%7D)
P' (-5,5), q' (10,5), r' (5,-15), s' (-10,-15) are the final coordinates.
The equation is:
8 x + 6 = 54, where x is the cost for each bracelet.
8 x = 54 - 6
8 x = 48
x = 48 : 8
x = 6
Answer:
The cost is $6.