Answer:
Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.
Step-by-step explanation:
Given:
Let
A(x₁ , y₁) = (1 , 4) and
B( x₂ , y₂ ) = (-1 , 2)
To Find:
θ = ?
Solution:
Slope of a line when two points are given is given bt
![Slope(AB)=\dfrac{y_{2}-y_{1} }{x_{2}-x_{1} }](https://tex.z-dn.net/?f=Slope%28AB%29%3D%5Cdfrac%7By_%7B2%7D-y_%7B1%7D%20%7D%7Bx_%7B2%7D-x_%7B1%7D%20%7D)
Substituting the values we get
![Slope(AB)=\dfrac{2-4}{-1-1}=\dfrac{-2}{-2}=1\\\\Slope=1](https://tex.z-dn.net/?f=Slope%28AB%29%3D%5Cdfrac%7B2-4%7D%7B-1-1%7D%3D%5Cdfrac%7B-2%7D%7B-2%7D%3D1%5C%5C%5C%5CSlope%3D1)
Also Slope of line when angle ' θ ' is given as
![Slope=\tan \theta](https://tex.z-dn.net/?f=Slope%3D%5Ctan%20%5Ctheta)
Substituting Slope = 1 we get
![1=\tan \theta](https://tex.z-dn.net/?f=1%3D%5Ctan%20%5Ctheta)
![\tan \theta=1\\\theta=\tan^{-1}(1)](https://tex.z-dn.net/?f=%5Ctan%20%5Ctheta%3D1%5C%5C%5Ctheta%3D%5Ctan%5E%7B-1%7D%281%29)
We Know That for angle 45°,
tan 45 = 1
Therefore
![\theta=45\°](https://tex.z-dn.net/?f=%5Ctheta%3D45%5C%C2%B0)
Therefore the angle that the line through the given pair of points makes with the positive direction of the x-axis is 45°.
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There are several ways to answer this. All involve finding a way to calculate the area of shapes we're familiar with and using those areas to find the area of this unusual shape. I've included three different ways, all of which yield the same total area.
In the first case, you cut the shape into two shapes by drawing a perpendicular line from point C to segment AE. That will give you a square and a trapezoid. The area of the square is (2 m)(5 m) = 10 m², and the area of the trapezoid is (0.5)(9 m - 5 m)(4 m + 4 m - 2 m) = 12 m². So the area of the entire shape is 10 m² + 12 m² = 22 m².
In the second case, you cut the shape into two shapes by drawing a perpendicular line from point C to segment AB. That will give you a rectangle and a triangle. The area of the rectangle is (2 m)(9 m) = 18 m². The area of the triangle is (0.5)(4 m - 2 m)(9 m - 5 m) = 4 m². So the area of the entire shape is 18 m² + 4 m² = 22 m².
In the third case, you can imagine that this shape is a piece of a larger rectangle with sides 4 m and 9 m with an area of 36 m². The area of this shape would be the difference between 36 m² and the area of the imaginary trapezoid that fills in rest of the rectangle. That trapezoid would have an area of (0.5)(4 m - 2 m)(9 m + 5 m) = 14 m². So the area of the shape given would be 36 m² - 14 m² = 22 m².
In any case, the area of the shape is 22 m².
Answer:
663
Step-by-step explanation:
Just divide
In this case 0 isn't between those numbers so the answer would be 5x0