Diego is building a kitchen table and a coffee table. The legs of a kitchen table must be twice the height of a coffee table and there are 4 legs on each table. He writes the expression 4(2x) + 4(x) to model his building plans. What does 2x represent?
2x represents the height of one kitchen table leg. 2x represents the total height of all four kitchen table legs. 2x represents the height of one coffee table leg.<span> 2x represents the total height of all four coffee table legs.</span>
True! Because T is the defining letter of the line, so it would be true!
Hope this helps!! :)
The answer is negative twelve -12
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Answer:
Third option is correct. Scale factor 3 ; enlargement.
Step-by-step explanation:
It is given that the figure A'B'C'D' is a dilation of figure ABCD.
We know that after dilation the corresponding sides of image and preimage are in the same proportion.
The image of AD is A'D'.
From the figure it is noticed that the A(-1,2), D(-1,-1), A'(-3,6) and D'(-3,-3).
Distance formula is
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
![AD=\sqrt{(-1+1)^2+(-1-2)^2}=\sqrt{9}=3](https://tex.z-dn.net/?f=AD%3D%5Csqrt%7B%28-1%2B1%29%5E2%2B%28-1-2%29%5E2%7D%3D%5Csqrt%7B9%7D%3D3)
![A'D'=\sqrt{(-3+3)^2+(-3-6)^2}=\sqrt{81}=9](https://tex.z-dn.net/?f=A%27D%27%3D%5Csqrt%7B%28-3%2B3%29%5E2%2B%28-3-6%29%5E2%7D%3D%5Csqrt%7B81%7D%3D9)
Scale factor is constant which represents the relation between image and preimage.
![k=\frac{A'D'}{AD}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7BA%27D%27%7D%7BAD%7D)
![k=\frac{9}{3}](https://tex.z-dn.net/?f=k%3D%5Cfrac%7B9%7D%7B3%7D)
![k=3](https://tex.z-dn.net/?f=k%3D3)
Therefore the scale factor is 3.
If k>0 it means enlargement and if k<0 it means reduction. Therefore third option is correct.
Answer:
a) SPAZ is equilateral.
b) Diagonals SA and PZ are perpendicular to each other.
c) Diagonals SA and PZ bisect each other.
Step-by-step explanation:
At first we form the triangle with the help of a graphing tool and whose result is attached below. It seems to be a paralellogram.
a) If figure is equilateral, then SP = PA = AZ = ZS:
![SP = \sqrt{[4-(-4)]^{2}+[(-2)-(-4)]^{2}}](https://tex.z-dn.net/?f=SP%20%3D%20%5Csqrt%7B%5B4-%28-4%29%5D%5E%7B2%7D%2B%5B%28-2%29-%28-4%29%5D%5E%7B2%7D%7D)
![SP \approx 8.246](https://tex.z-dn.net/?f=SP%20%5Capprox%208.246)
![PA = \sqrt{(6-4)^{2}+[6-(-2)]^{2}}](https://tex.z-dn.net/?f=PA%20%3D%20%5Csqrt%7B%286-4%29%5E%7B2%7D%2B%5B6-%28-2%29%5D%5E%7B2%7D%7D)
![PA \approx 8.246](https://tex.z-dn.net/?f=PA%20%5Capprox%20%208.246)
![AZ =\sqrt{(-2-6)^{2}+(4-6)^{2}}](https://tex.z-dn.net/?f=AZ%20%3D%5Csqrt%7B%28-2-6%29%5E%7B2%7D%2B%284-6%29%5E%7B2%7D%7D)
![AZ \approx 8.246](https://tex.z-dn.net/?f=AZ%20%5Capprox%208.246)
![ZS = \sqrt{[-4-(-2)]^{2}+(-4-4)^{2}}](https://tex.z-dn.net/?f=ZS%20%3D%20%5Csqrt%7B%5B-4-%28-2%29%5D%5E%7B2%7D%2B%28-4-4%29%5E%7B2%7D%7D)
![ZS \approx 8.246](https://tex.z-dn.net/?f=ZS%20%5Capprox%208.246)
Therefore, SPAZ is equilateral.
b) We use the slope formula to determine the inclination of diagonals SA and PZ:
![m_{SA} = \frac{6-(-4)}{6-(-4)}](https://tex.z-dn.net/?f=m_%7BSA%7D%20%3D%20%5Cfrac%7B6-%28-4%29%7D%7B6-%28-4%29%7D)
![m_{SA} = 1](https://tex.z-dn.net/?f=m_%7BSA%7D%20%3D%201)
![m_{PZ} = \frac{4-(-2)}{-2-4}](https://tex.z-dn.net/?f=m_%7BPZ%7D%20%3D%20%5Cfrac%7B4-%28-2%29%7D%7B-2-4%7D)
![m_{PZ} = -1](https://tex.z-dn.net/?f=m_%7BPZ%7D%20%3D%20-1)
Since
, diagonals SA and PZ are perpendicular to each other.
c) The diagonals bisect each other if and only if both have the same midpoint. Now we proceed to determine the midpoints of each diagonal:
![M_{SA} = \frac{1}{2}\cdot S(x,y) + \frac{1}{2}\cdot A(x,y)](https://tex.z-dn.net/?f=M_%7BSA%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20S%28x%2Cy%29%20%2B%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20A%28x%2Cy%29)
![M_{SA} = \frac{1}{2}\cdot (-4,-4)+\frac{1}{2}\cdot (6,6)](https://tex.z-dn.net/?f=M_%7BSA%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%28-4%2C-4%29%2B%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%286%2C6%29)
![M_{SA} = (-2,-2)+(3,3)](https://tex.z-dn.net/?f=M_%7BSA%7D%20%3D%20%28-2%2C-2%29%2B%283%2C3%29)
![M_{SA} = (1,1)](https://tex.z-dn.net/?f=M_%7BSA%7D%20%3D%20%281%2C1%29)
![M_{PZ} = \frac{1}{2}\cdot P(x,y) + \frac{1}{2}\cdot Z(x,y)](https://tex.z-dn.net/?f=M_%7BPZ%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20P%28x%2Cy%29%20%2B%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20Z%28x%2Cy%29)
![M_{PZ} = \frac{1}{2}\cdot (4,-2)+\frac{1}{2}\cdot (-2,4)](https://tex.z-dn.net/?f=M_%7BPZ%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%284%2C-2%29%2B%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%28-2%2C4%29)
![M_{PZ} = (2,-1)+(-1,2)](https://tex.z-dn.net/?f=M_%7BPZ%7D%20%3D%20%282%2C-1%29%2B%28-1%2C2%29)
![M_{PZ} = (1,1)](https://tex.z-dn.net/?f=M_%7BPZ%7D%20%3D%20%281%2C1%29)
Then, the diagonals SA and PZ bisect each other.