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KiRa [710]
2 years ago
6

Enter the coordinates of the point

Mathematics
1 answer:
agasfer [191]2 years ago
6 0

Answer: (\frac{\sqrt{3} }{2} ,-\frac{1}{2} )

Step-by-step explanation:

this forms a 30 degree reference angle

and this is in the 4th quadrant

When the angle is 30 degrees, the coordinates are:

(\frac{\sqrt{3} }{2} ,-\frac{1}{2} )

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(Geometry course question) Explain why it is not possible to construct an equilateral triangle that has
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Answer:

  √3 is irrational

Step-by-step explanation:

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<h3 /><h3>Location of point C</h3>

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<h3>Equilateral triangle</h3>

The line segments making up an equilateral triangle are separated by an angle of 60°. If two vertices are on grid squares, the third must be a rotation of one of them about the other through an angle of 60°. The rotation matrix is irrational, so the rotated point must have irrational coordinates.

The math of it is this. For rotation of (x, y) counterclockwise 60° about the origin, the transformation matrix is ...

  \left[\begin{array}{cc}\cos(60^\circ)&\sin(60^\circ)\\-\sin(60^\circ)&\cos(60^\circ)\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right]=\left[\begin{array}{c}x'\\y'\end{array}\right]

Cos(60°) is rational, but sin(60°) is not. For any non-zero rational values of x and y, the sum ...

  cos(60°)·x + sin(60°)·y

will be irrational.

As in the attached diagram, if one of the coordinates of the rotated point (B) is zero, then one of the coordinates of its image (C) will be rational. The other image point coordinate cannot be rational.

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Aleonysh [2.5K]
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zhuklara [117]

Answer:

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Step-by-step explanation:

There are 1000 liters in a kiloliter, so you would multiply both sides by 8.

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