If he could walk directly from the back door to the barn door, he would walk 10.2 yards less.
First, let's define our coordinate axis, I will use north as the y-axis and east as the x-axis.
So let's assume that Loto begins at the point (0, 0).
Then:
- He moves 8 yards east, to: (8yd, 0)
- He moves 6 yards north, to: (8yd, 6yd)
- He moves 12 yards east, to: (20yd, 6yd)
- He moves 5 yards north, to: (20yd, 11yd)
So he walked a total of 8yd + 6yd + 12yd + 5yd = 33yd
So he just moves from (0, 0) to (20yd, 11yd), thus the displacement is:
![D =\sqrt{(20yd - 0yd)^2 + (11yd - 0yd)^2} = 22.8ft](https://tex.z-dn.net/?f=D%20%20%3D%5Csqrt%7B%2820yd%20-%200yd%29%5E2%20%2B%20%2811yd%20-%200yd%29%5E2%7D%20%20%3D%2022.8ft)
So, if he could walk directly he would only walk 22.8 ft
The difference is:
33yd - 22.8yd = 10.2 yd.
He would walk 10.2 yards less if he could walk directly from the back door to the barn door.
If you want to learn more about displacements, you can read:
brainly.com/question/13271165
Answer:
x=11
Step-by-step explanation:
Since both angles are congruent, 2x-10=12, so x=11
A)
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) Q&({{ 0}}\quad ,&{{ 2}})\quad % (c,d) P&({{ 0.5}}\quad ,&{{ 0}}) \end{array}\qquad % distance value d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0AQ%26%28%7B%7B%200%7D%7D%5Cquad%20%2C%26%7B%7B%202%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%29%0AP%26%28%7B%7B%200.5%7D%7D%5Cquad%20%2C%26%7B%7B%200%7D%7D%29%0A%5Cend%7Barray%7D%5Cqquad%20%0A%25%20%20distance%20value%0Ad%20%3D%20%5Csqrt%7B%28%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%29%5E2%20%2B%20%28%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%29%5E2%7D)
![\bf QP=\sqrt{(0.5-0)^2+(0-2)^2}\implies QP=\sqrt{0.5^2+2^2} \\\\\\ QP=\sqrt{\left( \frac{1}{2} \right)^2+4}\implies QP=\sqrt{ \frac{1^2}{2^2}+4}\implies QP=\sqrt{\frac{1}{4}+4} \\\\\\ QP=\sqrt{\frac{17}{4}}\implies QP=\cfrac{\sqrt{17}}{\sqrt{4}}\implies QP=\cfrac{\sqrt{17}}{2}](https://tex.z-dn.net/?f=%5Cbf%20QP%3D%5Csqrt%7B%280.5-0%29%5E2%2B%280-2%29%5E2%7D%5Cimplies%20QP%3D%5Csqrt%7B0.5%5E2%2B2%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0AQP%3D%5Csqrt%7B%5Cleft%28%20%5Cfrac%7B1%7D%7B2%7D%20%5Cright%29%5E2%2B4%7D%5Cimplies%20QP%3D%5Csqrt%7B%20%5Cfrac%7B1%5E2%7D%7B2%5E2%7D%2B4%7D%5Cimplies%20QP%3D%5Csqrt%7B%5Cfrac%7B1%7D%7B4%7D%2B4%7D%0A%5C%5C%5C%5C%5C%5C%0AQP%3D%5Csqrt%7B%5Cfrac%7B17%7D%7B4%7D%7D%5Cimplies%20QP%3D%5Ccfrac%7B%5Csqrt%7B17%7D%7D%7B%5Csqrt%7B4%7D%7D%5Cimplies%20QP%3D%5Ccfrac%7B%5Csqrt%7B17%7D%7D%7B2%7D)
b)
since QR=QP, that means that QO is an angle bisector, and thus the segments it makes at the bottom of RO and OP, are also equal, thus RO=OP
thus, since the point P is 0.5 units away from the 0, point R is also 0.5 units away from 0 as well, however, is on the negative side, thus R (-0.5, 0)
c)
what's the equation of a line that passes through the points (-0.5, 0) and (0,2)?
![\bf \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) Q&({{ 0}}\quad ,&{{ 2}})\quad % (c,d) R&({{ -0.5}}\quad ,&{{ 0}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies \cfrac{{{ y_2}}-{{ y_1}}}{{{ x_2}}-{{ x_1}}}\implies \cfrac{0-2}{-0.5-0}\implies \cfrac{-2}{-0.5}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%20%28a%2Cb%29%0AQ%26%28%7B%7B%200%7D%7D%5Cquad%20%2C%26%7B%7B%202%7D%7D%29%5Cquad%20%0A%25%20%20%20%28c%2Cd%29%0AR%26%28%7B%7B%20-0.5%7D%7D%5Cquad%20%2C%26%7B%7B%200%7D%7D%29%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5C%5C%0A%25%20slope%20%20%3D%20m%0Aslope%20%3D%20%7B%7B%20m%7D%7D%3D%20%5Ccfrac%7Brise%7D%7Brun%7D%20%5Cimplies%20%0A%5Ccfrac%7B%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%7D%7B%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%7D%5Cimplies%20%5Ccfrac%7B0-2%7D%7B-0.5-0%7D%5Cimplies%20%5Ccfrac%7B-2%7D%7B-0.5%7D)