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alekssr [168]
2 years ago
12

Rotation 90° counterclockwise about the origin

Mathematics
1 answer:
alexandr402 [8]2 years ago
5 0
Draw a line from F to (0,0). If you rotate that line 90 degree counterclockwise about the origin, the coordinate of F’ will be (4,1)

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Please help?
Mazyrski [523]

Answer:

23\sqrt{3}\ un^2

Step-by-step explanation:

Connect points I and K, K and M, M and I.

1. Find the area of triangles IJK, KLM and MNI:

A_{\triangle IJK}=\dfrac{1}{2}\cdot IJ\cdot JK\cdot \sin 120^{\circ}=\dfrac{1}{2}\cdot 2\cdot 3\cdot \dfrac{\sqrt{3}}{2}=\dfrac{3\sqrt{3}}{2}\ un^2\\ \\ \\A_{\triangle KLM}=\dfrac{1}{2}\cdot KL\cdot LM\cdot \sin 120^{\circ}=\dfrac{1}{2}\cdot 8\cdot 2\cdot \dfrac{\sqrt{3}}{2}=4\sqrt{3}\ un^2\\ \\ \\A_{\triangle MNI}=\dfrac{1}{2}\cdot MN\cdot NI\cdot \sin 120^{\circ}=\dfrac{1}{2}\cdot 3\cdot 8\cdot \dfrac{\sqrt{3}}{2}=6\sqrt{3}\ un^2\\ \\ \\

2. Note that

A_{\triangle IJK}=A_{\triangle IAK}=\dfrac{3\sqrt{3}}{2}\ un^2 \\ \\ \\A_{\triangle KLM}=A_{\triangle KAM}=4\sqrt{3}\ un^2 \\ \\ \\A_{\triangle MNI}=A_{\triangle MAI}=6\sqrt{3}\ un^2

3. The area of hexagon IJKLMN is the sum of the area of all triangles:

A_{IJKLMN}=2\cdot \left(\dfrac{3\sqrt{3}}{2}+4\sqrt{3}+6\sqrt{3}\right)=23\sqrt{3}\ un^2

Another way to solve is to find the area of triangle KIM be Heorn's fomula, where all sides KI, KM and IM can be calculated using cosine theorem.

7 0
3 years ago
Name 3 things you would want to know about skin diseases/disorders?<br> PLEASE HELP
Gelneren [198K]

Answer:

Some skin disorders, like contact dermatitis, are temporary and relatively ... We'll help you identify common skin disorders, explain some treatment ... Here is a list of 25 with pictures. ... from the face down the body three to five days after first symptoms appear ... But what if they're actually a sign of an underlying condition.

Step-by-step explanation:

3 0
2 years ago
You might need:
Nastasia [14]

Answer:

11 + x

Step-by-step explanation:

A = LW

W = \frac{A}{L}

Plug in given information:

W = \frac{121-x^{2} }{11-x}

Factor the numerator:

W = \frac{(11+x)(11-x)}{(11-x)}

Cancel (11 - x):

W = 11 + x

5 0
3 years ago
Let f(x) = -12-31 +3 and g(x) = 3x - 3. Graph the functions in the same coordinate plane.
castortr0y [4]

Answer:

Zeros of Functions. A zero of a function f is a number a such that f(a) = 0. In other words, a zero of f is a solution for the equation f(x) = 0.

Step-by-step explanation:

5 0
2 years ago
Put these in order from least to greatest!: 88/25, 3.551, 3.88, 3 11/20
DedPeter [7]

Rewrite all 4 numbers as decimals to compare them:

88/25 = 3.52

3 11/20 = 3.55

Now arrange them in the correct order:

88/25, 3 11/20, 3.551, 3.88

7 0
2 years ago
Read 2 more answers
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